Details

analyze391.0ms (2.8%)

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%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
25%	25%	74.9%	0.1%	0%	0%	0%	6
25%	25%	74.9%	0.1%	0%	0%	0%	7
25%	25%	74.9%	0.1%	0%	0%	0%	8
25%	25%	74.9%	0.1%	0%	0%	0%	9
28.1%	25%	64%	0.1%	10.9%	0%	0%	10
36.4%	31.2%	54.6%	0.1%	14%	0%	0%	11
46.9%	39%	44.1%	0.1%	16.8%	0%	0%	12

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.3s (31.3%)

Results

1.3s	1839×	body	1024	valid
1.1s	5448×	body	256	valid
849.0ms	1634×	body	1024	infinite
388.0ms	962×	body	512	valid
357.0ms	805×	body	512	infinite
299.0ms	1475×	body	256	infinite
5.0ms	7×	body	2048	valid
1.0ms	1×	body	2048	infinite

Bogosity

preprocess18.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

180×	`fma-def`
140×	`*-commutative`
114×	`associate-/l*`
48×	`associate-r`
48×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (.f64 a2 a2)))
(.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (.f64 a1 a1)))
(.f64 (cos.f64 a2) (/.f64 (fma.f64 th th (.f64 a1 a1)) (sqrt.f64 2)))

Symmetry

(sort a1 a2)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

60×	`fma-def`
50×	`*-commutative`
40×	`associate-/l*`
18×	`associate-/r/`
16×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	30	35
2	56	35
3	79	35
4	106	35
5	124	35
6	142	35
7	147	35
8	149	35

Stop Event

1×

saturated

Counts

1 → 4

Calls

Call 1

Inputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

eval1.0ms (0%)

Compiler: Compiled 59 to 29 computations (50.8% saved)

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.07%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.24%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	1.17%	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 31 to 21 computations (32.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6%	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.68%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 41 to 16 computations (61% saved)

series11.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	a2	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	th	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	a1	@	-inf	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

rewrite83.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1078×	`associate-*r/`
856×	`associate-*l/`
790×	`associate-/r*`
596×	`associate-/l*`
430×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	280	56
2	3399	56

Stop Event

1×	node limit

Counts

2 → 155

Calls

Call 1

Inputs
(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 2 -1/2) (.f64 (.f64 a1 a1) 1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (.f64 a1 a1) 1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 -1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (cos.f64 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Outputs

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simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1322×	`associate-/l*`
708×	`distribute-frac-neg`
596×	`distribute-lft-in`
590×	`distribute-rgt-in`
572×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	435	9563
1	1120	9125
2	5292	8945

Stop Event

1×	node limit

Counts

215 → 253

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
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(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) 1) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) -1) (neg.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 a2 a2) 3) (pow.f64 (.f64 a1 a1) 3)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (+.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(/.f64 (*.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (cos.f64 th)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (cos.f64 th)) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 -1 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (cos.f64 th))) 1) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) 1) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))) (pow.f64 2 1/4))
(/.f64 (.f64 1 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (.f64 (hypot.f64 a1 a2) (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))) (pow.f64 2 1/4))
(/.f64 (.f64 (sqrt.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (hypot.f64 a1 a2))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (hypot.f64 a1 a2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (cos.f64 th))) 1) (sqrt.f64 2))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) 1) (pow.f64 2 1/4))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (cos.f64 th))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
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(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 2 -1/2))
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(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 2 -1/2))
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(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.86%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	1.2%	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series4.0ms (0%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	th	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a1	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a1	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	th	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	th	@	0	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite100.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1226×	`associate-/r*`
844×	`associate-/l*`
836×	`distribute-rgt-in`
794×	`distribute-lft-in`
310×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	299	48
2	4071	48

Stop Event

1×	node limit

Counts

2 → 205

Calls

Call 1

Inputs
(/.f64 (cos.f64 th) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/2) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (cos.f64 th)) (/.f64 -1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) 1) (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)) 1) (.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1 (.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) 1)) (.f64 1 (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) 1) 1) (.f64 (.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (.f64 (sqrt.f64 2) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 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Outputs

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(cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (neg.f64 (sqrt.f64 2))) (-.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (sqrt.f64 2))) (+.f64 (pow.f64 a2 4) 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (neg.f64 (cos.f64 th))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1) (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))))))

simplify113.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1310×	`associate-/l*`
826×	`associate-/r*`
810×	`times-frac`
764×	`associate-r`
744×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	604	13879
1	1684	13845

Stop Event

1×	node limit

Counts

245 → 327

Calls

Call 1

Inputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)
(*.f64 (cos.f64 th) (pow.f64 2 -1/2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))
(*.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2)))
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(/.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (neg.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (sqrt.f64 (cos.f64 th)))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) 1)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 2)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 2)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) -1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (pow.f64 2 1/4))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (neg.f64 (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (sqrt.f64 2))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (cos.f64 th)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (neg.f64 (cos.f64 th))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 2))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (neg.f64 (cos.f64 th))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 2))
(log.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))

Outputs
(/.f64 1 (sqrt.f64 2))
(+.f64 (*.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
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(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (cos.f64 th) (*.f64 (sqrt.f64 (cbrt.f64 2)) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 (cbrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (*.f64 (sqrt.f64 (pow.f64 2 1/4)) (sqrt.f64 (pow.f64 2 1/4))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (sqrt.f64 (pow.f64 2 1/4))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 (pow.f64 2 1/4))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (cbrt.f64 2))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 2))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (cbrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) (.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 2 1/4))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (pow.f64 2 1/4))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (pow.f64 2 1/4))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))
(/.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (neg.f64 (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (*.f64 (-.f64 a1 a2) (sqrt.f64 2)))))
(/.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (sqrt.f64 2))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (cos.f64 th)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (*.f64 (-.f64 a1 a2) (sqrt.f64 2)))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (*.f64 (-.f64 a1 a2) (sqrt.f64 2)))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (neg.f64 (cos.f64 th))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (*.f64 (-.f64 a1 a2) (sqrt.f64 2)))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (neg.f64 (cos.f64 th))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (neg.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (cos.f64 th))))
(/.f64 (/.f64 (neg.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))))
(.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (/.f64 (neg.f64 (cos.f64 th)) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 3)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3) 1/3)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 2))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 2) (pow.f64 (hypot.f64 a1 a2) 4)))
(log.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 1))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))

eval214.0ms (1.5%)

Compiler: Compiled 12607 to 7579 computations (39.9% saved)

prune184.0ms (1.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	562	18	580
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	564	18	582

Error

Counts

582 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.72%	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
▶	1.12%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	37.87%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	47.95%	(/.f64 (.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
	42.99%	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	45.92%	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	42.55%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
▶	46.23%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	43.01%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	45.95%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	37.93%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	1.03%	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	1.8%	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	42.97%	(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
▶	45.92%	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	42.97%	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	45.86%	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
	1.04%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

Compiler

Compiled 530 to 378 computations (28.7% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.34%	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.35%	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
✓	0.61%	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))

Compiler

Compiled 41 to 20 computations (51.2% saved)

series25.0ms (0.2%)

Counts

3 → 76

Calls

21 calls:

Time	Variable		Point	Expression
6.0ms	a1	@	0	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
5.0ms	a2	@	0	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
2.0ms	a1	@	0	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))
1.0ms	th	@	0	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))
1.0ms	a1	@	inf	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))

rewrite125.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1258×	`associate-/r/`
930×	`swap-sqr`
866×	`associate-/l/`
482×	`distribute-lft-neg-in`
430×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	81
1	275	75
2	3661	75

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs
(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(/.f64 (sqrt.f64 2) (cos.f64 th))

Outputs

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a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 1 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 a1 a2)) (*.f64 (sqrt.f64 (hypot.f64 a1 a2)) (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 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1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 1 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (/.f64 1 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (neg.f64 (/.f64 -1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (neg.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (cos.f64 th)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (cos.f64 th) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))))

simplify175.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1320×	`associate-r`
1260×	`*-commutative`
1136×	`associate-/r*`
1110×	`associate-l`
1066×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	856	16990
1	2577	16732

Stop Event

1×	node limit

Counts

304 → 419

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/2 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))))))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4))))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 3) (cos.f64 th)))) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) a2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 3) (cos.f64 th)))) (+.f64 (.f64 -1 (.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/4 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 5)))) (.f64 -1/8 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 5))))))) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) a2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 (pow.f64 a2 3) (cos.f64 th)))) (+.f64 (.f64 -1 (.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/4 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 5)))) (.f64 -1/8 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 a2 5))))))) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 7) (cos.f64 th)))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 5) (cos.f64 th)))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 5) (cos.f64 th))))) (pow.f64 a2 2)))) (pow.f64 a1 6))) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) a2)))))
(/.f64 (sqrt.f64 2) (*.f64 a1 (cos.f64 th)))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 3) (cos.f64 th)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th))) (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th)))) (pow.f64 a1 5))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (*.f64 (pow.f64 a1 3) (cos.f64 th))))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th))) (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th)))) (pow.f64 a1 5))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 6)) (cos.f64 th))) (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th))) (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (cos.f64 th)))) (pow.f64 a2 2)))) (pow.f64 a1 7))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 (pow.f64 a1 3) (cos.f64 th)))))))
(.f64 -1 (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th))))
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(.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))) (sqrt.f64 (hypot.f64 a1 a2)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 (hypot.f64 a1 a2)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) -1) (neg.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) 1)) (cos.f64 th))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (.f64 (sqrt.f64 2) (/.f64 1 (hypot.f64 a1 a2)))) (cos.f64 th))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (cos.f64 th))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (hypot.f64 a1 a2)) (cos.f64 th)))) (sqrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) 1) (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (pow.f64 2 1/4)) (sqrt.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) 1) (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (cbrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) -1)
(neg.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(neg.f64 (.f64 (hypot.f64 a1 a2) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))
(neg.f64 (.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(neg.f64 (.f64 1 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(*.f64 (sqrt.f64 2) (/.f64 1 (cos.f64 th)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 -1 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(*.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (neg.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 (cos.f64 th))))
(*.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (cos.f64 th)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(*.f64 (/.f64 1 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(*.f64 -1 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 -1 (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 2 1/4) (cos.f64 th)) (pow.f64 2 1/4))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (cbrt.f64 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3) 1/3)
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1)
(neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))) 1))
(sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3))
(cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (cos.f64 th) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 th th))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4)))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (neg.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) -5/24) (pow.f64 th 4)))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 th th))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (neg.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 -5/24 (pow.f64 th 4))))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/2 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))))))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4))))))
(fma.f64 -1 (.f64 (fma.f64 1/48 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (fma.f64 -1/720 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) -5/24)))) (pow.f64 th 6)) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (neg.f64 (.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) -5/24) (pow.f64 th 4))))))
(fma.f64 -1 (.f64 (fma.f64 1/48 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (fma.f64 -1/720 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) -5/48))) (pow.f64 th 6)) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 th th))) (fma.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (neg.f64 (.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))) (*.f64 -5/24 (pow.f64 th 4)))))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
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(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) -1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(neg.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(neg.f64 (.f64 (hypot.f64 a1 a2) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(neg.f64 (.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(neg.f64 (.f64 1 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (sqrt.f64 2) (/.f64 1 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 -1 (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 (cos.f64 th))))
(.f64 (pow.f64 2 1/4) (.f64 (/.f64 1 (cos.f64 th)) (pow.f64 2 1/4)))
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (neg.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 (cos.f64 th))))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))))
(*.f64 (/.f64 1 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 1 (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 (/.f64 (*.f64 (sqrt.f64 2) 1) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (cos.f64 th)))
(*.f64 -1 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (cos.f64 th)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (/.f64 -1 (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(.f64 (pow.f64 2 1/4) (.f64 (/.f64 1 (cos.f64 th)) (pow.f64 2 1/4)))
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 2 1/4) (cos.f64 th)) (pow.f64 2 1/4))
(.f64 (pow.f64 2 1/4) (.f64 (/.f64 1 (cos.f64 th)) (pow.f64 2 1/4)))
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
(/.f64 (*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(.f64 (pow.f64 2 1/4) (.f64 (/.f64 1 (cos.f64 th)) (pow.f64 2 1/4)))
(*.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (cbrt.f64 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 2) (.f64 (/.f64 1 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 2)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 3)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3) 1/3)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1)
(/.f64 (sqrt.f64 2) (cos.f64 th))
(neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(/.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (cos.f64 th)))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))) 1))
(/.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (cos.f64 th)))
(sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (*.f64 (/.f64 2 (pow.f64 (cos.f64 th) 3)) (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.68%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))

Compiler

Compiled 31 to 12 computations (61.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
0.0ms	a1	@	inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
0.0ms	a2	@	inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
0.0ms	a1	@	0	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
0.0ms	a2	@	-inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1010×	`associate-*r/`
990×	`*-commutative`
778×	`associate-/r*`
752×	`associate-*l/`
616×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	233	23
2	3053	23

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 a2 a2)) (*.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)) (*.f64 (pow.f64 2 -1/2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)) (*.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)) (*.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 -1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (+.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (*.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (*.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))) (*.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))))))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1186×	`associate-*r/`
872×	`associate-/l*`
778×	`associate-+r-`
756×	`associate-+l-`
752×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2637
1	401	2549
2	1536	2479
3	6966	2479

Stop Event

1×	node limit

Counts

75 → 78

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))
(+.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))) 1)
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)))
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) 1))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))
(.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (+.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
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(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 8) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2)))
(.f64 1 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)) (sqrt.f64 2))) (+.f64 (pow.f64 a2 8) (-.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (sqrt.f64 2) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)))) (+.f64 (pow.f64 a2 8) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (sqrt.f64 2) (+.f64 (pow.f64 (.f64 a2 a2) 6) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)))) (fma.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (+.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))) (pow.f64 a2 8)))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))
(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.13%	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
✓	0.5%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

Compiler

Compiled 28 to 15 computations (46.4% saved)

series4.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
1.0ms	th	@	-inf	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
1.0ms	th	@	inf	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
0.0ms	a1	@	0	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
0.0ms	th	@	0	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))

rewrite95.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1226×	`associate-*r/`
1100×	`associate-/r*`
1014×	`*-commutative`
892×	`associate-/l*`
862×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	224	44
2	2848	44

Stop Event

1×	node limit

Counts

2 → 190

Calls

Call 1

Inputs
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 a1) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)) (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 -1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 a1 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) (/.f64 a1 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (cbrt.f64 (sqrt.f64 2))) (/.f64 a1 (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 2)) (*.f64 a1 (neg.f64 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 1) (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 2) a1)) (sqrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (sqrt.f64 a1))) (sqrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))) (neg.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2))) (cbrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (sqrt.f64 2) a1)) (cbrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (*.f64 a1 a1) (/.f64 -1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 1 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 a1 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 (*.f64 a1 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (*.f64 (*.f64 a1 a1) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (*.f64 (*.f64 a1 a1) (cbrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th))) (/.f64 (sqrt.f64 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th)))) (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th)))) (cbrt.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th))))) (/.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 a1 (*.f64 a1 (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (cos.f64 th) 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neg.f64 (*.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))

simplify108.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1496×	`associate-/l*`
904×	`associate-/l/`
620×	`times-frac`
582×	`distribute-rgt-in`
576×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	489	7722
1	1322	7494
2	6225	7494

Stop Event

1×	node limit

Counts

226 → 265

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) 1)
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(.f64 (.f64 a1 a1) (pow.f64 2 -1/2))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 1)
(.f64 1 (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(*.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)) (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(.f64 (pow.f64 2 -1/2) (.f64 a1 a1))
(.f64 (.f64 a1 (neg.f64 a1)) (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 a1 4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a1 (sqrt.f64 2)) (/.f64 a1 1))
(*.f64 (/.f64 a1 (cbrt.f64 (sqrt.f64 2))) (/.f64 a1 (cbrt.f64 2)))
(.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 a1 (neg.f64 a1)))
(*.f64 (/.f64 a1 1) (/.f64 a1 (sqrt.f64 2)))
(*.f64 (/.f64 a1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 2 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 2) a1)) (sqrt.f64 a1))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (sqrt.f64 a1))) (sqrt.f64 a1))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))) (neg.f64 a1))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2))) (cbrt.f64 a1))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (sqrt.f64 2) a1)) (cbrt.f64 a1))
(pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) -1)
(neg.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)))
(neg.f64 (*.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)) 1))
(neg.f64 (.f64 (.f64 a1 a1) (/.f64 -1 (sqrt.f64 2))))
(neg.f64 (*.f64 1 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))
(sqrt.f64 (/.f64 (pow.f64 a1 4) 2))
(log.f64 (exp.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a1 (.f64 a1 (cos.f64 th)))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (sqrt.f64 (cos.f64 th))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 (.f64 a1 a1) (sqrt.f64 (cos.f64 th)))))
(/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)) (cbrt.f64 (cos.f64 th))))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 (.f64 a1 a1) (cbrt.f64 (cos.f64 th)))))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (/.f64 (sqrt.f64 2) 1))
(/.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th)))
(/.f64 (sqrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th)))) (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th))))))
(/.f64 (.f64 (cbrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th)))) (cbrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th))))) (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))))))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (*.f64 a1 a1)))
(/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (pow.f64 2 1/4))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 a1 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 (cos.f64 th)))))
(/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (pow.f64 2 1/4) (*.f64 a1 a1)))
(/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 a1)))
(/.f64 (.f64 (cos.f64 th) (sqrt.f64 a1)) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 a1))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a1 (/.f64 1 a1))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (cbrt.f64 2) a1))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) -1) (neg.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (*.f64 (cos.f64 th) (neg.f64 a1)) (neg.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 1 (.f64 a1 (cos.f64 th))) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 1 (/.f64 (.f64 a1 a1) (/.f64 1 (cos.f64 th)))) (sqrt.f64 2))
(/.f64 (.f64 1 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))) (pow.f64 2 1/4))
(/.f64 (.f64 1 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (/.f64 a1 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th))))) (pow.f64 2 1/4))
(/.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th))))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (/.f64 1 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (/.f64 1 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) -1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) a1) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
(/.f64 (.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 a1)) (sqrt.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 (*.f64 a1 (neg.f64 a1)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (.f64 (cos.f64 th) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2))) 1) (cbrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
(/.f64 (.f64 (.f64 (cos.f64 th) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2))) (cbrt.f64 a1)) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 (.f64 (cos.f64 th) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2))) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (cos.f64 th) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2))) (cbrt.f64 (*.f64 a1 (neg.f64 a1)))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) a1) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) 1) (/.f64 (sqrt.f64 2) (.f64 a1 a1)))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) (sqrt.f64 a1)) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 a1))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) (.f64 a1 (neg.f64 a1))) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 a1 (/.f64 1 a1))) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 a1 (/.f64 (cbrt.f64 2) a1))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) -1) (neg.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (*.f64 (/.f64 (cos.f64 th) 1) (neg.f64 a1)) (neg.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (.f64 a1 a1)) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 a1) 2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(/.f64 (.f64 (sqrt.f64 a1) (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 a1))))
(/.f64 (.f64 -1 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (*.f64 (/.f64 a1 (/.f64 1 a1)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (cos.f64 th)) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 a1 (/.f64 (cbrt.f64 2) a1)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a1) (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 (.f64 a1 (cos.f64 th)) 1) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (.f64 a1 a1) (/.f64 1 (cos.f64 th))) 1) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) 1) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a1 a1))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th)))) (.f64 (/.f64 a1 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))) (pow.f64 2 1/4))
(/.f64 (.f64 a1 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (.f64 1 (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4))) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a1 a1))))
(/.f64 (.f64 (sqrt.f64 a1) (/.f64 (.f64 a1 (cos.f64 th)) (pow.f64 2 1/4))) (sqrt.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (.f64 (sqrt.f64 (.f64 a1 (neg.f64 a1))) (/.f64 (*.f64 a1 (cos.f64 th)) (pow.f64 2 1/4))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cbrt.f64 (.f64 a1 (.f64 a1 (cos.f64 th)))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 a1)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) (/.f64 (pow.f64 2 1/4) a1))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (cbrt.f64 (pow.f64 a1 4)))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4)))) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) a1)) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2)) (/.f64 1 a1))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) 1) (/.f64 (sqrt.f64 2) a1))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 (/.f64 (sqrt.f64 2) a1))) (sqrt.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (/.f64 (.f64 a1 (cos.f64 th)) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a1)) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 1 (sqrt.f64 a1))) (/.f64 (sqrt.f64 2) (sqrt.f64 a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 1 (pow.f64 (cbrt.f64 a1) 2))) (/.f64 (sqrt.f64 2) (cbrt.f64 a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) 1)) (/.f64 (pow.f64 2 1/4) a1))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (sqrt.f64 a1))) (/.f64 (pow.f64 2 1/4) (sqrt.f64 a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (cbrt.f64 2) 1)) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (cbrt.f64 2) (sqrt.f64 a1))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a1) 2))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 a1)))
(/.f64 (/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 a1)))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) 1) (sqrt.f64 2))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) 1) (pow.f64 2 1/4))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a1 a1))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a1 a1))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a1 a1))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a1 a1))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a1 a1))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(pow.f64 (*.f64 (/.f64 a1 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)
(neg.f64 (*.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)) (cos.f64 th)))
(neg.f64 (*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))
(neg.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))
(expm1.f64 (log1p.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(exp.f64 (log.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (/.f64 (.f64 -1/2 (.f64 a1 (.f64 a1 (.f64 th th)))) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(fma.f64 -1/2 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 th th)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (/.f64 (.f64 1/24 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))))
(fma.f64 -1/2 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 th th)) (fma.f64 -1/720 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (pow.f64 th 6)) (fma.f64 a1 (/.f64 a1 (sqrt.f64 2)) (/.f64 (.f64 1/24 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
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(neg.f64 (*.f64 (/.f64 (cos.f64 th) 1) (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(cbrt.f64 (.f64 (pow.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(exp.f64 (log.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.43%	(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
✓	1.13%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))

Compiler

Compiled 28 to 15 computations (46.4% saved)

series1.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	0	(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
0.0ms	th	@	0	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
0.0ms	th	@	inf	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
0.0ms	a1	@	inf	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
0.0ms	th	@	-inf	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))

rewrite94.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1798×	`associate-/l*`
1502×	`associate-*l/`
1102×	`*-commutative`
588×	`associate-/r/`
394×	`associate-/l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	230	44
2	3092	44

Stop Event

1×	node limit

Counts

2 → 151

Calls

Call 1

Inputs
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 (cos.f64 th) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) 1) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) (/.f64 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (neg.f64 (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (*.f64 (cos.f64 th) (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a1 -2)) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 (cos.f64 th)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a1 -2)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) -1) (neg.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (neg.f64 (/.f64 (sqrt.f64 2) a1))) (neg.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 (sqrt.f64 a1)))) (sqrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 (pow.f64 (cbrt.f64 a1) 2)))) (cbrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (/.f64 a1 (/.f64 1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1) (neg.f64 (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (cos.f64 th)) -1) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) a1))) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)) (neg.f64 (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) 1) 1) (/.f64 (*.f64 a1 a1) (sqrt.f64 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (cbrt.f64 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1))) (cbrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a1 -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 a1 -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) a1) (/.f64 (pow.f64 2 1/4) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) a1) (/.f64 1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 a1 -2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) 1) (pow.f64 a1 -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 a1) (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 1 (cbrt.f64 (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1)) (neg.f64 (/.f64 (pow.f64 2 1/4) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (neg.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (*.f64 a1 a1))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) a1) (/.f64 (cbrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) 1) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (*.f64 a1 a1)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (*.f64 a1 a1)) (/.f64 (pow.f64 2 1/4) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) a1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (cbrt.f64 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (*.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 a1 (/.f64 (cbrt.f64 2) a1))) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))) (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))) (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))) (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1))) (/.f64 (pow.f64 2 1/4) a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (pow.f64 a1 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (*.f64 a1 a1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))))))

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1400×	`unswap-sqr`
694×	`distribute-rgt-in`
678×	`distribute-lft-in`
578×	`distribute-lft-neg-in`
542×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	363	5879
1	1059	5741
2	3874	5741

Stop Event

1×	node limit

Counts

187 → 225

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 1)
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 1)
(.f64 1 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4)))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (cos.f64 th) 1))
(.f64 (neg.f64 (.f64 a1 a1)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))
(.f64 (/.f64 (cos.f64 th) 1) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) (/.f64 a1 (pow.f64 2 1/4)))
(.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 a1 -2)))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (/.f64 (cos.f64 th) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 (cos.f64 th) a1))
(*.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 a1 -2)) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))
(.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1)
(.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (neg.f64 (.f64 a1 a1)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 (cos.f64 th) (neg.f64 (*.f64 a1 a1))))
(*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a1 -2)))
(*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a1 -2)) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (sqrt.f64 (cos.f64 th)) 1))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a1 -2)))
(*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a1 -2)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)))
(.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a1 a1)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1))
(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1))
(.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a1))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(.f64 (neg.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) -1) (neg.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(*.f64 (/.f64 (cos.f64 th) (neg.f64 (/.f64 (sqrt.f64 2) a1))) (neg.f64 a1))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 a1)))) (sqrt.f64 a1))
(.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 (pow.f64 (cbrt.f64 a1) 2)))) (cbrt.f64 a1))
(.f64 (/.f64 1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (.f64 a1 a1))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (/.f64 a1 (/.f64 1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1) (neg.f64 (.f64 a1 a1)))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) -1) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) a1))) a1)
(.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)) (neg.f64 (.f64 a1 a1)))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) 1) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (pow.f64 2 1/4)) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (cbrt.f64 2)) (/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) a1)) a1)
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (sqrt.f64 2))) (neg.f64 (.f64 a1 a1)))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) 1)) (.f64 a1 a1))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (.f64 a1 (sqrt.f64 a1)))) (sqrt.f64 a1))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (.f64 a1 (pow.f64 (cbrt.f64 a1) 2)))) (cbrt.f64 a1))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) -1) (neg.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (/.f64 (sqrt.f64 2) a1))) (neg.f64 a1))
(.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) 1) (sqrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (.f64 a1 a1))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a1)) (sqrt.f64 (/.f64 (sqrt.f64 2) a1))) (sqrt.f64 a1))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) 1) (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (.f64 a1 a1))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a1))) (cbrt.f64 a1))
(pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 1)
(pow.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3) 1/3)
(pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a1 -2)) -1)
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (.f64 a1 a1))))
(sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4))))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) 1)
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)
(.f64 1 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))
(*.f64 (/.f64 (pow.f64 2 1/4) a1) (/.f64 (pow.f64 2 1/4) a1))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))
(*.f64 (/.f64 (sqrt.f64 2) a1) (/.f64 1 a1))
(*.f64 (pow.f64 a1 -2) (sqrt.f64 2))
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (pow.f64 a1 -2)))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (.f64 a1 a1))))
(.f64 (.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)) (pow.f64 2 1/4))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)) (cbrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 2) 1) (pow.f64 a1 -2))
(*.f64 (/.f64 1 a1) (/.f64 (sqrt.f64 2) a1))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 1 (cbrt.f64 (pow.f64 a1 4))))
(.f64 -1 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))
(*.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1)) (neg.f64 (/.f64 (pow.f64 2 1/4) a1)))
(.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (neg.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(.f64 (/.f64 1 (neg.f64 (.f64 a1 a1))) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)))
(.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) a1) (/.f64 (cbrt.f64 2) a1))
(.f64 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) 1) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)) (pow.f64 2 1/4))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)) (/.f64 (pow.f64 2 1/4) 1))
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))))
(*.f64 (/.f64 (cbrt.f64 2) a1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))
(.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (cbrt.f64 2) 1))
(.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (/.f64 (cbrt.f64 2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 1 (/.f64 a1 (/.f64 (cbrt.f64 2) a1))) (cbrt.f64 (sqrt.f64 2)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))) (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))) (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))) (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))
(*.f64 (neg.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1))) (/.f64 (pow.f64 2 1/4) a1))
(.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3) 1/3)
(pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) -1)
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))
(sqrt.f64 (/.f64 2 (pow.f64 a1 4)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3))
(cbrt.f64 (/.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 (.f64 a1 a1) 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 th th)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 th th)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 th th)) (fma.f64 1/24 (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 th 4)) a1)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 th th)) (fma.f64 -1/720 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (pow.f64 th 6)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 th th)) (fma.f64 -1/720 (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (pow.f64 th 6)) (fma.f64 1/24 (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 th 4)) a1)) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
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(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (neg.f64 (.f64 a1 a1))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a1 4))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a1 4)))
(sqrt.f64 (*.f64 (pow.f64 a1 4) (/.f64 (pow.f64 (cos.f64 th) 2) 2)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))) 1)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 1 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (/.f64 (pow.f64 2 1/4) a1) (/.f64 (pow.f64 2 1/4) a1))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)))
(*.f64 (pow.f64 a1 -2) (pow.f64 2 1/2))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 a1 -2) (cbrt.f64 2)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (pow.f64 a1 -2)))
(*.f64 (/.f64 (sqrt.f64 2) a1) (/.f64 1 a1))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (pow.f64 a1 -2) (sqrt.f64 2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (pow.f64 a1 -2)))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (.f64 a1 a1))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 (.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)) (pow.f64 2 1/4))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (pow.f64 a1 -2)))
(*.f64 (pow.f64 a1 -2) (pow.f64 2 1/2))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a1 -2)) (cbrt.f64 2))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (pow.f64 a1 -2) (cbrt.f64 2)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 (cbrt.f64 2) (pow.f64 a1 -2)))
(*.f64 (/.f64 (sqrt.f64 2) 1) (pow.f64 a1 -2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (/.f64 1 a1) (/.f64 (sqrt.f64 2) a1))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (pow.f64 (cbrt.f64 a1) 2))
(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 (pow.f64 a1 4)))
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 1 (cbrt.f64 (pow.f64 a1 4))))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (pow.f64 (cbrt.f64 a1) 2))
(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 (pow.f64 a1 4)))
(.f64 -1 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1)) (neg.f64 (/.f64 (pow.f64 2 1/4) a1)))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4)))) (neg.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (/.f64 1 (neg.f64 (.f64 a1 a1))) (neg.f64 (sqrt.f64 2)))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) a1) (/.f64 (cbrt.f64 2) a1))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) 1) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)) (pow.f64 2 1/4))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a1 a1)) (/.f64 (pow.f64 2 1/4) 1))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)))
(/.f64 (*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 a1 4)))
(/.f64 (/.f64 (pow.f64 2 1/2) (cbrt.f64 (pow.f64 a1 4))) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a1 4))))
(/.f64 (*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 a1 4)))
(/.f64 (/.f64 (pow.f64 2 1/2) (cbrt.f64 (pow.f64 a1 4))) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (/.f64 (cbrt.f64 2) a1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a1))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (cbrt.f64 2) 1))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a1 4))))
(.f64 (/.f64 (cbrt.f64 2) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(*.f64 (/.f64 1 (/.f64 a1 (/.f64 (cbrt.f64 2) a1))) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (.f64 a1 a1)))
(.f64 (cbrt.f64 2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))) (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))) (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))) (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2)))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(*.f64 (neg.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a1))) (/.f64 (pow.f64 2 1/4) a1))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a1 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 1)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(pow.f64 (/.f64 (pow.f64 2 1/4) a1) 2)
(/.f64 (pow.f64 2 1/2) (*.f64 a1 a1))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))) 3)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3) 1/3)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) -1)
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a1 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(sqrt.f64 (/.f64 2 (pow.f64 a1 4)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 a1 -2)))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2)) 3))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(cbrt.f64 (/.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 (.f64 a1 a1) 3)))
(cbrt.f64 (*.f64 (/.f64 2 (pow.f64 a1 6)) (sqrt.f64 2)))
(cbrt.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 6) 2)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(*.f64 (sqrt.f64 2) (pow.f64 a1 -2))

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.34%	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.91%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series1.0ms (0%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	th	@	0	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
0.0ms	a2	@	0	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
0.0ms	a2	@	inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
0.0ms	a1	@	inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
0.0ms	a2	@	-inf	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1790×	`associate-/l*`
802×	`associate-/r/`
652×	`associate-/l/`
606×	`distribute-lft-in`
310×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	299	33
2	4065	33

Stop Event

1×	node limit

Counts

1 → 72

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a2 a1) (*.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (*.f64 (/.f64 (hypot.f64 a2 a1) 1) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) 1) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)) (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) -1) (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (/.f64 (cos.f64 th) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) -1) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) -1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (+.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (*.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (*.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))) (*.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1108×	`associate-/l/`
1090×	`distribute-lft-in`
1078×	`distribute-rgt-in`
990×	`associate-/r/`
416×	`distribute-lft-neg-out`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	265	4880
1	771	4650
2	3269	4650

Stop Event

1×	node limit

Counts

108 → 129

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(.f64 1 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (hypot.f64 a2 a1) (.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a2 a1) 2))
(.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (cos.f64 th))
(.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (cos.f64 th))))
(.f64 (.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (.f64 (/.f64 (hypot.f64 a2 a1) 1) (cos.f64 th)))
(.f64 (/.f64 (hypot.f64 a2 a1) 1) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)) (hypot.f64 a2 a1))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 1 (cos.f64 th))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) -1) (neg.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (cos.f64 th))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (/.f64 (cos.f64 th) 1))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) -1) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) -1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (+.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))
(.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(pow.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) -1)
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))

Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
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(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))

eval529.0ms (3.8%)

Compiler: Compiled 25836 to 15389 computations (40.4% saved)

prune321.0ms (2.3%)

Pruning

26 alts after pruning (22 fresh and 4 done)

	Pruned	Kept	Total
New	1176	14	1190
Fresh	5	8	13
Picked	0	1	1
Done	1	3	4
Total	1182	26	1208

Error

Counts

1208 → 26

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.12%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	37.87%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
▶	42.55%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
	42.93%	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	62.68%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	45.92%	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	62.51%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
✓	46.23%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	42.53%	(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
	62.65%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	45.86%	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
	62.47%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	37.74%	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	45.93%	(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
▶	43.01%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	62.62%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
▶	62.45%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	37.93%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	1.03%	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	1.8%	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
✓	45.92%	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	42.97%	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	45.86%	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
	1.04%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	45.89%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
	60.38%	(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2))

Compiler

Compiled 601 to 452 computations (24.8% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.31%	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
✓	0.86%	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 46 to 21 computations (54.3% saved)

series5.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	th	@	0	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	th	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	th	@	inf	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
0.0ms	a2	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	th	@	-inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite82.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`associate-*r/`
774×	`distribute-rgt-in`
728×	`distribute-lft-in`
630×	`associate-*l/`
328×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	320	48
2	4124	48

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(*.f64 (pow.f64 2 -1/2) (cos.f64 th))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1) (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a1 a1) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a1 a1) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (*.f64 a2 a2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1)) (*.f64 1 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 1/2)) (*.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (sqrt.f64 1/2)) (*.f64 (*.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1) 1) (*.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))) (-.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 3) (pow.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 3)) (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (-.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (neg.f64 (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (neg.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))) (-.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 3) (pow.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 3))) (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (-.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (hypot.f64 a1 a2)) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (hypot.f64 a1 a2)) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (sqrt.f64 (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (cbrt.f64 (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (neg.f64 (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (neg.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))) 1) (-.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 3) (pow.f64 (*.f64 (cos.f64 th) 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 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(cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))))

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

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

846×	`associate-r`
844×	`associate-/l*`
778×	`distribute-lft-neg-in`
778×	`distribute-rgt-neg-in`
768×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	7601
1	861	7031
2	5047	6673

Stop Event

1×	node limit

Counts

141 → 152

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
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(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(fma.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(fma.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)
(pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3))
(cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (.f64 (sqrt.f64 1/2) 1/2)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Outputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -1/2)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (+.f64 (.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2)))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (*.f64 (sqrt.f64 1/2) -1/2))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 th th) -1/2) (.f64 (pow.f64 th 4) 1/24)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (pow.f64 th 6))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 6))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -1/2)))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (+.f64 (.f64 (.f64 th th) -1/2) (.f64 (pow.f64 th 6) -1/720))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (sqrt.f64 1/2))
(.f64 (+.f64 (.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)))
(+.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 th th) -1/2) (.f64 (pow.f64 th 4) 1/24))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (+.f64 (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)) (.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6)))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6)) (sqrt.f64 1/2))))
(+.f64 (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (pow.f64 th 6) -1/720) (.f64 (*.f64 th th) -1/2))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
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(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (fma.f64 a1 a1 (neg.f64 (*.f64 a2 a2))))
(/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (sqrt.f64 (fma.f64 a1 a1 (neg.f64 (.f64 a2 a2))))) (sqrt.f64 (fma.f64 a1 a1 (neg.f64 (.f64 a2 a2)))))
(/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (.f64 (cbrt.f64 (fma.f64 a1 a1 (neg.f64 (.f64 a2 a2)))) (cbrt.f64 (fma.f64 a1 a1 (neg.f64 (.f64 a2 a2)))))) (cbrt.f64 (fma.f64 a1 a1 (neg.f64 (.f64 a2 a2)))))
(/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2))) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)))
(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) (hypot.f64 a1 a2)) 2)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 2))
(fabs.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 3))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))
(fma.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(fma.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) 1/3)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))
(sqrt.f64 (*.f64 1/2 (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 1/2)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (cos.f64 th) 3)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (.f64 (sqrt.f64 1/2) 1/2)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.22%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.62%	(/.f64 a1 (sqrt.f64 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	inf	(/.f64 a1 (sqrt.f64 2))
0.0ms	a1	@	-inf	(/.f64 a1 (sqrt.f64 2))
0.0ms	a1	@	0	(/.f64 a1 (sqrt.f64 2))
0.0ms	a1	@	0	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
0.0ms	a1	@	-inf	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1604×	`add-sqr-sqrt`
1584×	`*-un-lft-identity`
1478×	`add-cube-cbrt`
1458×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	164	28
2	2009	28

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a1 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a1) (*.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (*.f64 a1 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) a1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 a1 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 a1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))))))

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1190×	`associate-*r/`
900×	`unswap-sqr`
880×	`associate-/l*`
712×	`associate-+r-`
670×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	1080
1	296	1068
2	1246	1068
3	7098	1068

Stop Event

1×	node limit

Counts

66 → 69

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 a1 (sqrt.f64 2)))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a1 a1) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) a1)
(*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (*.f64 a1 a1) 2))
(log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))) 1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)
(/.f64 a1 (sqrt.f64 2))
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(/.f64 a1 (sqrt.f64 2))
(*.f64 1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 a1 (pow.f64 2 -1/2))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a1 a1) 2)))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 a1 (/.f64 2 a1))))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (.f64 a1 (/.f64 a1 2))))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 a1 (/.f64 2 a1))))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (.f64 a1 (/.f64 a1 2))))
(*.f64 (pow.f64 2 -1/2) a1)
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 (/.f64 a1 (sqrt.f64 2)))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)))
(pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
(/.f64 a1 (sqrt.f64 2))
(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(sqrt.f64 (/.f64 (*.f64 a1 a1) 2))
(sqrt.f64 (/.f64 a1 (/.f64 2 a1)))
(sqrt.f64 (*.f64 a1 (/.f64 a1 2)))
(log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 a1 (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))
(/.f64 a1 (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))
(/.f64 a1 (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))) 1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (/.f64 (cbrt.f64 2) a1)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a1 (cbrt.f64 (sqrt.f64 2))) (/.f64 a1 (cbrt.f64 2)))
(/.f64 (*.f64 a1 (/.f64 a1 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.48%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	inf	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.0ms	a2	@	0	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.0ms	a2	@	-inf	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1588×	`add-sqr-sqrt`
1568×	`*-un-lft-identity`
1464×	`add-cube-cbrt`
1448×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	164	17
2	2068	17

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

Inputs
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (*.f64 a2 (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)) (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 a2 4)) (*.f64 (cbrt.f64 (*.f64 a2 a2)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) a2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (cbrt.f64 (*.f64 a2 a2)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (*.f64 a2 a2)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 a2 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))))))

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1496×	`associate-r`
1238×	`associate-+r+`
1226×	`associate-l`
1116×	`associate-+l+`
624×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	992
1	221	980
2	792	980
3	4996	980

Stop Event

1×	node limit

Counts

46 → 45

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))) 1)
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
(.f64 (.f64 a2 a2) (pow.f64 2 -1/2))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)
(.f64 1 (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)) (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(.f64 (cbrt.f64 (pow.f64 a2 4)) (.f64 (cbrt.f64 (*.f64 a2 a2)) (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (cbrt.f64 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 a2 a2)) (pow.f64 2 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(neg.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(exp.f64 (log.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 a2 a2) (pow.f64 2 -1/2))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 1 (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(.f64 (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)) (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 a2 4) 2)))
(.f64 (cbrt.f64 (pow.f64 a2 4)) (.f64 (cbrt.f64 (*.f64 a2 a2)) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (pow.f64 a2 4)) (.f64 (pow.f64 2 -1/2) (cbrt.f64 (*.f64 a2 a2))))
(.f64 (pow.f64 2 -1/2) (.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 (*.f64 a2 a2))))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 a2 (/.f64 a2 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) a2)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 a2 (/.f64 a2 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) a2)
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (cbrt.f64 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (cbrt.f64 (.f64 a2 a2)) (sqrt.f64 2)))
(/.f64 (cbrt.f64 (*.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4))))
(/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (sqrt.f64 2) (cbrt.f64 (*.f64 a2 a2))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 a2 a2)) (pow.f64 2 1/4)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (cbrt.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)))
(pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 3)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3) 1/3)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(neg.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2) 3))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2)) 1))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.74%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	1.2%	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 27 to 15 computations (44.4% saved)

series8.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	th	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
1.0ms	th	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
1.0ms	th	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.0ms	a2	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.0ms	a2	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1030×	`*-commutative`
922×	`associate-*r/`
848×	`associate-/r*`
782×	`unswap-sqr`
754×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	224	27
2	2793	27

Stop Event

1×	node limit

Counts

1 → 113

Calls

Call 1

Inputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (*.f64 (*.f64 a2 a2) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (*.f64 a2 (sqrt.f64 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (*.f64 (*.f64 a2 a2) (cbrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (pow.f64 a2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (*.f64 a2 (cbrt.f64 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 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(cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) -1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) 1) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) 1) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 a2) a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (*.f64 a2 a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))))))

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1222×	`associate-/l*`
752×	`associate-/l/`
730×	`unswap-sqr`
540×	`times-frac`
452×	`distribute-frac-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	5051
1	930	5043
2	4970	4899

Stop Event

1×	node limit

Counts

137 → 170

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))) 1)
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)
(/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cos.f64 th)))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (sqrt.f64 (cos.f64 th))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (sqrt.f64 (cos.f64 th)))))
(/.f64 (sqrt.f64 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (*.f64 a2 (sqrt.f64 a2))))
(/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cbrt.f64 (cos.f64 th))))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (cbrt.f64 (cos.f64 th)))))
(/.f64 (cbrt.f64 (*.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (pow.f64 a2 4))))
(/.f64 (cbrt.f64 (.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (.f64 a2 (cbrt.f64 a2))))
(/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (*.f64 a2 a2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) 1))
(/.f64 (neg.f64 (cos.f64 th)) (/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 a2 a2)))
(/.f64 (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(/.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)))))
(/.f64 (*.f64 a2 (sqrt.f64 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 a2)))
(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2))
(/.f64 (.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 a2 a2))))
(/.f64 (.f64 a2 (cbrt.f64 (.f64 a2 a2))) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 a2)))
(/.f64 (.f64 (.f64 a2 a2) (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) (sqrt.f64 2))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (pow.f64 2 1/4))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (.f64 a2 (sqrt.f64 (cos.f64 th)))))
(/.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 1 (cos.f64 th)))
(/.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a2 a2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(/.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) 1)) (sqrt.f64 2))
(/.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a2 a2) -1) (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(/.f64 (.f64 1 (/.f64 (cos.f64 th) (/.f64 1 (.f64 a2 a2)))) (sqrt.f64 2))
(/.f64 (.f64 1 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))) (pow.f64 2 1/4))
(/.f64 (.f64 1 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a2 a2)))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) (pow.f64 2 1/4))
(/.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4))) (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (/.f64 1 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (/.f64 1 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) -1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (cos.f64 th))) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (neg.f64 (cos.f64 th)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2))) 1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2))) (cbrt.f64 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2))) (cbrt.f64 (neg.f64 (cos.f64 th)))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (cos.f64 th) 1) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (.f64 a2 a2)) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(/.f64 (.f64 -1 (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(/.f64 (.f64 (.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 (cos.f64 th) (/.f64 1 (.f64 a2 a2))) 1) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2))) 1) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a2 a2))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (pow.f64 2 1/4))
(/.f64 (.f64 1 (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (pow.f64 2 1/4))
(/.f64 (.f64 (sqrt.f64 (neg.f64 (cos.f64 th))) (/.f64 (.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (cbrt.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (*.f64 a2 a2) 1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (/.f64 (.f64 a2 a2) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 1 (sqrt.f64 (cos.f64 th)))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 2) 1)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (cos.f64 th))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) 1) (sqrt.f64 2))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) 1) (pow.f64 2 1/4))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a2 a2))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)
(pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) 3)
(pow.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3) 1/3)
(neg.f64 (.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (.f64 a2 a2)))
(neg.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 a2) a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3))
(cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (.f64 a2 a2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(exp.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (*.f64 a2 a2)) (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (*.f64 a2 a2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (*.f64 a2 a2)) (sqrt.f64 2))))))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 -1/720 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 th 6) (.f64 a2 a2))))) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))) 1)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cos.f64 th)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (sqrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (sqrt.f64 (cos.f64 th)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (*.f64 a2 (sqrt.f64 a2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cbrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (cbrt.f64 (cos.f64 th)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (cbrt.f64 (*.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (pow.f64 a2 4))))
(/.f64 (cbrt.f64 (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a2 4)))))
(.f64 (/.f64 (cbrt.f64 (.f64 a2 a2)) (sqrt.f64 2)) (*.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a2 4))))
(/.f64 (cbrt.f64 (.f64 a2 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (.f64 a2 (cbrt.f64 a2))))
(.f64 (/.f64 (cbrt.f64 (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (*.f64 a2 (cbrt.f64 a2)))
(.f64 (cbrt.f64 a2) (/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (.f64 a2 a2)))))
(/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (*.f64 a2 a2))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (.f64 a2 a2)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) 1))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (neg.f64 (cos.f64 th)) (/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 a2 a2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 a2 (sqrt.f64 a2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (sqrt.f64 a2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (cbrt.f64 (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (cbrt.f64 (.f64 a2 a2))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (.f64 a2 a2)))
(/.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (*.f64 a2 a2))))
(/.f64 (.f64 a2 (cbrt.f64 (.f64 a2 a2))) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 a2)))
(.f64 (/.f64 (cbrt.f64 (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (*.f64 a2 (cbrt.f64 a2)))
(.f64 (cbrt.f64 a2) (/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (.f64 a2 a2)))))
(/.f64 (.f64 (.f64 a2 a2) (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (pow.f64 2 1/4))
(/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
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(.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))))))
(/.f64 (/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) a2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) 1) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 2 1/2))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) -1) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 2 1/2))
(/.f64 (/.f64 (.f64 (cos.f64 th) (neg.f64 (.f64 a2 a2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) 1) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 1 (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) 1) (pow.f64 2 1/4))
(/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 2 1/2))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (pow.f64 2 1/4)) (*.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (pow.f64 2 1/4))) (/.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (*.f64 a2 a2) (/.f64 (pow.f64 2 1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 2 1/2))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (pow.f64 2 1/4)) (*.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 2))))
(.f64 (/.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) a2) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (sqrt.f64 (cbrt.f64 2))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (cbrt.f64 2))) (*.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 2 1/4))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (pow.f64 2 1/4))) (/.f64 (.f64 (/.f64 a2 (cbrt.f64 2)) a2) (cbrt.f64 (pow.f64 2 1/4))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (.f64 a2 a2))) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 a2 a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) (*.f64 a2 a2))) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (cbrt.f64 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 2))))
(.f64 (/.f64 a2 (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 2))))
(pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) 3)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3) 1/3)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (.f64 a2 a2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(neg.f64 (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))
(sqrt.f64 (*.f64 (pow.f64 a2 4) (/.f64 (pow.f64 (cos.f64 th) 2) 2)))
(sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a2 4))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 a2) a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(cbrt.f64 (.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (.f64 a2 a2) 3)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.13%	(.f64 a2 (.f64 a2 (cos.f64 th)))
✓	0.2%	(*.f64 a2 (cos.f64 th))
✓	0.5%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))

Compiler

Compiled 29 to 12 computations (58.6% saved)

series3.0ms (0%)

Counts

3 → 64

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(*.f64 a2 (cos.f64 th))
0.0ms	a2	@	inf	(*.f64 a2 (cos.f64 th))
0.0ms	th	@	0	(.f64 a2 (.f64 a2 (cos.f64 th)))
0.0ms	a2	@	inf	(.f64 a2 (.f64 a2 (cos.f64 th)))
0.0ms	th	@	0	(*.f64 a2 (cos.f64 th))

rewrite114.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1694×	`associate-/r*`
1510×	`associate-/l*`
1102×	`*-commutative`
932×	`associate-*r/`
640×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	224	55
2	2866	55

Stop Event

1×	node limit

Counts

3 → 99

Calls

Call 1

Inputs
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(*.f64 a2 (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 2) 2)) (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 (cos.f64 th) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) (/.f64 -1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (*.f64 a2 (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 1 (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))) (/.f64 1 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 a2 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th))) (/.f64 a2 (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) (*.f64 a2 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 (cos.f64 th) (/.f64 1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (sqrt.f64 2)) (*.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 1) (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (/.f64 1 a2)) (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 (*.f64 a2 (cos.f64 th)) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 1 (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) 1) (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (cbrt.f64 2)) (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (cbrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (sqrt.f64 2)) (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))) (sqrt.f64 a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 a2 (cos.f64 th))))) (sqrt.f64 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (neg.f64 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 2)))) (cbrt.f64 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 2))) (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))) (cbrt.f64 a2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (*.f64 a2 a2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a2 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) a2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 a2 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (cos.f64 th))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 a2 3) (pow.f64 (*.f64 a2 (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))))

simplify129.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1328×	`associate-/r*`
1188×	`associate-/l/`
1038×	`distribute-rgt-in`
1034×	`distribute-lft-in`
926×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	275	4707
1	738	4553
2	3208	4553

Stop Event

1×	node limit

Counts

163 → 171

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
(*.f64 (cos.f64 th) a2)
a2
(+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) a2)) a2)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) a2)) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) a2)) a2))
(+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) a2)) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) a2)) (+.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) a2)) a2)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2))) (.f64 -1/720 (.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(-.f64 (exp.f64 (log1p.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))))) 1)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (.f64 a2 (cos.f64 th)) (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (pow.f64 2 -1/2))
(.f64 (.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)
(.f64 1 (.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2))))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))))
(.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) 2) 2)))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 2) 2)) (cbrt.f64 (.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)))
(.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))) (/.f64 -1 (sqrt.f64 2)))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (.f64 a2 (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 1 (sqrt.f64 (cos.f64 th)))))
(.f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2))
(.f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2) 1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) 1))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2))))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2))) (/.f64 1 (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) a2)
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)) (/.f64 a2 1))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(*.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 (cos.f64 th) (/.f64 1 a2)))
(.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 (cos.f64 th) (neg.f64 (*.f64 a2 a2))))
(.f64 (/.f64 a2 1) (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (/.f64 1 a2)) (/.f64 a2 (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 2)))
(*.f64 (/.f64 a2 (/.f64 1 (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) 1) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) (pow.f64 2 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (pow.f64 2 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (cbrt.f64 2)) (cbrt.f64 (.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 (/.f64 (.f64 a2 a2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a2 a2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (/.f64 (.f64 a2 a2) (cbrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (sqrt.f64 2)) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))))
(.f64 (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))) (sqrt.f64 a2))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 a2 (cos.f64 th))))) (sqrt.f64 (*.f64 a2 (cos.f64 th))))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (neg.f64 (.f64 a2 (cos.f64 th))))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (.f64 a2 (cos.f64 th)) 2)))) (cbrt.f64 (*.f64 a2 (cos.f64 th))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2))) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (cos.f64 th))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))) (cbrt.f64 a2))
(pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) 2)
(pow.f64 (cbrt.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (.f64 a2 a2))) -1)
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 2) 2))
(log.f64 (exp.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(exp.f64 (log.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (cos.f64 th)))) 1)
(pow.f64 (*.f64 a2 (cos.f64 th)) 1)
(pow.f64 (sqrt.f64 (*.f64 a2 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) a2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 a2 3)))
(expm1.f64 (log1p.f64 (*.f64 a2 (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 a2 (cos.f64 th))))
(log1p.f64 (expm1.f64 (*.f64 a2 (cos.f64 th))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) 1)
(pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 1)
(pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 3)
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 2))
(log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (cos.f64 th))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3))
(cbrt.f64 (.f64 (pow.f64 a2 3) (pow.f64 (.f64 a2 (cos.f64 th)) 3)))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))

Outputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (.f64 -1/2 (.f64 th th)) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (.f64 -1/2 (.f64 th th)) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (pow.f64 th 4))) a2) (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a2 a2)) (sqrt.f64 2)))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (*.f64 a2 a2)) (sqrt.f64 2))))))
(fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (pow.f64 th 4))) a2) (fma.f64 (/.f64 a2 (sqrt.f64 2)) a2 (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (.f64 (/.f64 (.f64 -1/720 (pow.f64 th 6)) (/.f64 (sqrt.f64 2) a2)) a2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
(*.f64 (cos.f64 th) a2)
(*.f64 a2 (cos.f64 th))
a2
(+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) a2)) a2)
(fma.f64 -1/2 (.f64 a2 (.f64 th th)) a2)
(+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) a2)) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) a2)) a2))
(fma.f64 -1/2 (.f64 a2 (.f64 th th)) (fma.f64 1/24 (*.f64 a2 (pow.f64 th 4)) a2))
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(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (sqrt.f64 2)))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 2)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (sqrt.f64 2)))) (/.f64 a2 (cbrt.f64 2)))
(*.f64 (/.f64 a2 (/.f64 1 (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(.f64 a2 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))))
(.f64 a2 (.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (/.f64 a2 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))))
(.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))))
(.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 (/.f64 a2 (cbrt.f64 2)) (*.f64 a2 (sqrt.f64 (cos.f64 th)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 a2 (cbrt.f64 2)) (.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th)))) (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))))
(.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th)))) (.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 (/.f64 a2 (cbrt.f64 2)) (*.f64 a2 (sqrt.f64 (cos.f64 th)))) (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 a2 (cbrt.f64 2)) (.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) 1) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) (sqrt.f64 2)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) (pow.f64 2 1/4)))
(/.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4))) (cos.f64 th))
(.f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (pow.f64 2 1/4)))
(/.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4))) (cos.f64 th))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (cbrt.f64 2)) (cbrt.f64 (.f64 a2 (/.f64 (*.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 2) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (.f64 a2 (*.f64 a2 (cos.f64 th)))) 2) (cbrt.f64 2)))
(.f64 (cbrt.f64 (.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))) (/.f64 (pow.f64 (cbrt.f64 (.f64 a2 (*.f64 a2 (cos.f64 th)))) 2) (cbrt.f64 2)))
(.f64 (/.f64 (.f64 a2 a2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(/.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(/.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))
(*.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4))) (cos.f64 th))
(.f64 (/.f64 (.f64 a2 a2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (sqrt.f64 2)))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (/.f64 (.f64 a2 a2) (cbrt.f64 2)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (sqrt.f64 2)))) (/.f64 a2 (cbrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2) (sqrt.f64 2)) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))) (sqrt.f64 a2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (sqrt.f64 (.f64 a2 (cos.f64 th))))) (sqrt.f64 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (neg.f64 (.f64 a2 (cos.f64 th))))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (.f64 (neg.f64 a2) (cos.f64 th)))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (.f64 (cos.f64 th) (neg.f64 a2)))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (.f64 a2 (cos.f64 th)) 2)))) (cbrt.f64 (*.f64 a2 (cos.f64 th))))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cbrt.f64 (pow.f64 (.f64 a2 (cos.f64 th)) 2)) (cbrt.f64 (.f64 a2 (cos.f64 th)))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 2))) (cbrt.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (cos.f64 th))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))) (cbrt.f64 a2))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 1)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (sqrt.f64 (cos.f64 th)))) 2)
(pow.f64 (*.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a2 (pow.f64 2 1/4))) 2)
(pow.f64 (cbrt.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))) 3)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3) 1/3)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (.f64 a2 a2))) -1)
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(neg.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (.f64 (neg.f64 a2) (cos.f64 th)))
(.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (.f64 (cos.f64 th) (neg.f64 a2)))
(sqrt.f64 (/.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 2) 2))
(sqrt.f64 (/.f64 (pow.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) 2) 2))
(log.f64 (exp.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))) 3))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(expm1.f64 (log1p.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(exp.f64 (log.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (cos.f64 th)))) 1)
(*.f64 a2 (cos.f64 th))
(pow.f64 (*.f64 a2 (cos.f64 th)) 1)
(*.f64 a2 (cos.f64 th))
(pow.f64 (sqrt.f64 (*.f64 a2 (cos.f64 th))) 2)
(*.f64 a2 (cos.f64 th))
(pow.f64 (cbrt.f64 (*.f64 a2 (cos.f64 th))) 3)
(*.f64 a2 (cos.f64 th))
(pow.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3) 1/3)
(*.f64 a2 (cos.f64 th))
(sqrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 2))
(fabs.f64 (*.f64 a2 (cos.f64 th)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) a2))
(*.f64 a2 (cos.f64 th))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (cos.f64 th)))))
(*.f64 a2 (cos.f64 th))
(cbrt.f64 (pow.f64 (*.f64 a2 (cos.f64 th)) 3))
(*.f64 a2 (cos.f64 th))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 a2 3)))
(*.f64 a2 (cos.f64 th))
(expm1.f64 (log1p.f64 (*.f64 a2 (cos.f64 th))))
(*.f64 a2 (cos.f64 th))
(exp.f64 (log.f64 (*.f64 a2 (cos.f64 th))))
(*.f64 a2 (cos.f64 th))
(log1p.f64 (expm1.f64 (*.f64 a2 (cos.f64 th))))
(*.f64 a2 (cos.f64 th))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) 1)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 1)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 3)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3) 1/3)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(sqrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 2))
(fabs.f64 (.f64 a2 (.f64 a2 (cos.f64 th))))
(log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (cos.f64 th))))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(cbrt.f64 (.f64 (pow.f64 a2 3) (pow.f64 (.f64 a2 (cos.f64 th)) 3)))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))

eval270.0ms (1.9%)

Compiler: Compiled 11360 to 6568 computations (42.2% saved)

prune240.0ms (1.7%)

Pruning

30 alts after pruning (25 fresh and 5 done)

	Pruned	Kept	Total
New	647	16	663
Fresh	8	9	17
Picked	0	1	1
Done	4	4	8
Total	659	30	689

Error

Counts

689 → 30

Alt Table

Click to see full alt table

Status	Error	Program
	62.75%	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
✓	1.12%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	37.87%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	66.21%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	42.55%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
✓	62.68%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	45.92%	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	62.51%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	62.65%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	45.86%	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
	62.47%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	62.59%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	62.47%	(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
▶	62.63%	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
	45.93%	(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
▶	62.62%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	62.45%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	37.93%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	62.48%	(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
▶	42.48%	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	62.5%	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	85.75%	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
▶	37.74%	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	45.87%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
▶	42.86%	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	42.49%	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	45.89%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
	42.48%	(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
	62.68%	(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
	75.07%	(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))

Compiler

Compiled 653 to 501 computations (23.3% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.59%	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 31 to 12 computations (61.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a1	@	0	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a1	@	inf	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a2	@	0	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.0ms	a1	@	-inf	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

rewrite66.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1008×	`*-commutative`
908×	`unswap-sqr`
588×	`swap-sqr`
558×	`associate-*r/`
494×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	233	23
2	3025	23

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4))) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3)) (-.f64 (+.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (*.f64 (+.f64 a1 a2) (neg.f64 (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (-.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4)))) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3))) (-.f64 (+.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2)) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2)) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 1/2)) (*.f64 (+.f64 a1 a2) (neg.f64 (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 1/2)) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4))) 1) (*.f64 (sqrt.f64 1/2) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3)) 1) (-.f64 (+.f64 (*.f64 1/2 (pow.f64 a1 4)) (*.f64 1/2 (pow.f64 a2 4))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (*.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))) (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (+.f64 a1 a2)) (-.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (*.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 1/2 1/4) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))))

simplify94.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1666×	`associate-/l*`
1052×	`associate-/r*`
896×	`*-commutative`
620×	`associate-/l/`
570×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3421
1	514	3253
2	2230	3217
3	7961	3217

Stop Event

1×	node limit

Counts

75 → 86

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)
(/.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 1/2)))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 1/2)))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (-.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3)) (-.f64 (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (sqrt.f64 1/2) (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (.f64 (+.f64 a1 a2) (neg.f64 (-.f64 a1 a2))))
(/.f64 (.f64 (sqrt.f64 1/2) (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (.f64 1 (-.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4)))) (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 1 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3))) (-.f64 (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2)) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2)) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 1/2)) (.f64 (+.f64 a1 a2) (neg.f64 (-.f64 a1 a2))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 1/2)) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (.f64 (-.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) 1) (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3)) 1) (-.f64 (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (sqrt.f64 1/2) (hypot.f64 a1 a2))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))) (sqrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (cbrt.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2))) (cbrt.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))) (cbrt.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(pow.f64 (*.f64 (pow.f64 1/2 1/4) (hypot.f64 a1 a2)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)
(sqrt.f64 (*.f64 1/2 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(cbrt.f64 (.f64 (.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(fma.f64 (.f64 a1 a1) (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (*.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (sqrt.f64 1/2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))))
(.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 1/2)))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (+.f64 a1 a2) (-.f64 a1 a2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))))
(.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2)))))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (-.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 a1 a2) (-.f64 a1 a2))))
(/.f64 (.f64 1/2 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (*.f64 (sqrt.f64 1/2) (+.f64 a2 a1)) (-.f64 a1 a2)))
(.f64 (/.f64 1/2 (sqrt.f64 1/2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 a1 a2)) (/.f64 1/2 (.f64 (sqrt.f64 1/2) (+.f64 a2 a1))))
(/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3)) (-.f64 (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 1/2 (pow.f64 a2 4))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))
(/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3)) (-.f64 (.f64 1/2 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))))
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(/.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (+.f64 a1 a2)) (-.f64 a1 a2))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (+.f64 a2 a1) (-.f64 a1 a2))))
(.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 (neg.f64 a2)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))
(pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (*.f64 (pow.f64 1/2 1/4) (hypot.f64 a1 a2)) 2)
(pow.f64 (*.f64 (hypot.f64 a1 a2) (pow.f64 1/2 1/4)) 2)
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 1/2 1/2))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(sqrt.f64 (*.f64 1/2 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
(sqrt.f64 (*.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(cbrt.f64 (.f64 (.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(fma.f64 (.f64 a1 a1) (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)))

localize49.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	0.67%	(/.f64 a2 (sqrt.f64 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	inf	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	0	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	-inf	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	0	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
0.0ms	a2	@	inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1604×	`add-sqr-sqrt`
1584×	`*-un-lft-identity`
1478×	`add-cube-cbrt`
1458×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	164	28
2	2009	28

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 a2 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a2) (*.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 a2) 2) (*.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (*.f64 a2 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) a2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) a2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 a2 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a2 (/.f64 (sqrt.f64 2) a2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 a2) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))))))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1190×	`associate-*r/`
900×	`unswap-sqr`
880×	`associate-/l*`
712×	`associate-+r-`
670×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	1080
1	296	1068
2	1246	1068
3	7098	1068

Stop Event

1×	node limit

Counts

66 → 69

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2)))) 1)
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 a2 (sqrt.f64 2)))
(.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a2 a2) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) a2)
(*.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) a2) -1)
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (*.f64 a2 a2) 2))
(log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) 1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2)))) 1)
(/.f64 a2 (sqrt.f64 2))
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(/.f64 a2 (sqrt.f64 2))
(*.f64 1 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 a2 (pow.f64 2 -1/2))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a2 a2) 2)))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 a2 (/.f64 2 a2))))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (.f64 a2 (/.f64 a2 2))))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 a2 (/.f64 2 a2))))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (.f64 a2 (/.f64 a2 2))))
(*.f64 (pow.f64 2 -1/2) a2)
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a2) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a2 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a2) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a2 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)))
(pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) a2) -1)
(/.f64 a2 (sqrt.f64 2))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(sqrt.f64 (/.f64 (*.f64 a2 a2) 2))
(sqrt.f64 (/.f64 a2 (/.f64 2 a2)))
(sqrt.f64 (*.f64 a2 (/.f64 a2 2)))
(log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 a2 (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))
(/.f64 a2 (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))) 1))
(/.f64 a2 (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) 1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(/.f64 (*.f64 a2 (/.f64 a2 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

localize27.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.47%	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))

Compiler

Compiled 19 to 13 computations (31.6% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
0.0ms	a2	@	inf	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
0.0ms	a2	@	-inf	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1418×	`add-sqr-sqrt`
1392×	`*-un-lft-identity`
1300×	`add-cube-cbrt`
1286×	`add-cbrt-cube`
1272×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	167	17
2	1917	17

Stop Event

1×	node limit

Counts

1 → 12

Calls

Call 1

Inputs
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (pow.f64 a2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))))

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1436×	`distribute-rgt-in`
1418×	`distribute-lft-in`
1210×	`log-prod`
782×	`associate-r`
674×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	410
1	99	410
2	376	410
3	2055	410

Stop Event

1×	node limit

Counts

24 → 17

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 3)
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) 1/3)
(sqrt.f64 (*.f64 1/2 (pow.f64 a2 4)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (*.f64 a2 a2)))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 a2 a2) (pow.f64 2 -1/2))
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 3)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) 1/3)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(sqrt.f64 (*.f64 1/2 (pow.f64 a2 4)))
(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))

localize24.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.01%	(.f64 -1/2 (.f64 th th))
✓	0.16%	(.f64 (+.f64 (.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2))
✓	5.17%	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 67 to 33 computations (50.7% saved)

series5.0ms (0%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	th	@	0	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
1.0ms	th	@	inf	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
1.0ms	a1	@	0	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	a2	@	0	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite106.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1644×	`associate-*r/`
1344×	`associate-*l/`
382×	`add-sqr-sqrt`
368×	`pow1`
368×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	83
1	379	81
2	4843	81

Stop Event

1×	node limit

Counts

3 → 151

Calls

Call 1

Inputs
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (+.f64 (.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2))
(.f64 -1/2 (.f64 th th))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 (*.f64 th th)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (*.f64 -1/2 th) th 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (*.f64 -1/2 th) th 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 1/4 (pow.f64 th 4)) (fma.f64 -1/2 (*.f64 th th) -1)) (+.f64 (/.f64 1 (fma.f64 -1/2 (*.f64 th th) -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/2 (*.f64 th th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 th (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 -1/2 (*.f64 th th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/4 (pow.f64 th 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 th) th) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 -1/2 (*.f64 th th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 -1/2 (*.f64 th th))))))))

simplify140.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1054×	`associate-r`
954×	`associate-l`
704×	`associate-/l*`
480×	`*-commutative`
470×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	421	12513
1	1168	11533
2	6123	11533

Stop Event

1×	node limit

Counts

211 → 245

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(+.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(+.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))
(+.f64 (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 1) (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1))
(+.f64 (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1) (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 1))
(-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1)
(/.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(/.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (fma.f64 -1/2 (.f64 th th) -1) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)))
(/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th)))) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2)))
(/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (.f64 a1 a2) 2)))
(/.f64 (-.f64 (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))) (.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))) (-.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))))
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(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (sqrt.f64 1/2)) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (sqrt.f64 1/2)) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 1 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (sqrt.f64 1/2))) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 1 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (sqrt.f64 1/2))) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 1 (.f64 1/4 (pow.f64 th 4)))) (-.f64 1 (.f64 -1/2 (.f64 th th))))
(/.f64 (.f64 (sqrt.f64 1/2) (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (neg.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (.f64 (sqrt.f64 1/2) (neg.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (neg.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (sqrt.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (sqrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (fma.f64 (.f64 -1/2 th) th 1)) 2)) (cbrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (cbrt.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (fma.f64 (.f64 -1/2 th) th 1)) 2)) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (.f64 (-.f64 1 (.f64 1/4 (pow.f64 th 4))) (sqrt.f64 1/2)) (-.f64 1 (.f64 -1/2 (.f64 th th))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (sqrt.f64 1/2)) (neg.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (.f64 (neg.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (sqrt.f64 1/2)) (neg.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) 1) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) 1) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (sqrt.f64 1/2)) 1) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (sqrt.f64 1/2)) 1) (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (sqrt.f64 1/2))) (sqrt.f64 (+.f64 1 (-.f64 (.f64 1/4 (pow.f64 th 4)) (.f64 -1/2 (.f64 th th))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (sqrt.f64 1/2))) (sqrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(pow.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) 1)
(pow.f64 (.f64 (pow.f64 1/2 1/4) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) 3) 1/3)
(sqrt.f64 (.f64 1/2 (pow.f64 (fma.f64 (.f64 -1/2 th) th 1) 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (fma.f64 (*.f64 -1/2 th) th 1)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)))))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 (.f64 -1/2 th) th 1) 3) (*.f64 1/2 (sqrt.f64 1/2))))
(cbrt.f64 (.f64 (.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (fma.f64 (*.f64 -1/2 th) th 1) 3)))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))))
(exp.f64 (log.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (sqrt.f64 1/2))) 1))
(log1p.f64 (expm1.f64 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (sqrt.f64 1/2))))
(+.f64 (.f64 -1/2 (.f64 th th)) 0)
(+.f64 1 (fma.f64 -1/2 (*.f64 th th) -1))
(-.f64 (fma.f64 (*.f64 -1/2 th) th 1) 1)
(-.f64 (exp.f64 (log1p.f64 (fma.f64 (*.f64 -1/2 th) th 1))) 2)
(-.f64 (/.f64 (.f64 1/4 (pow.f64 th 4)) (fma.f64 -1/2 (.f64 th th) -1)) (+.f64 (/.f64 1 (fma.f64 -1/2 (*.f64 th th) -1)) 1))
(pow.f64 (.f64 -1/2 (.f64 th th)) 1)
(pow.f64 (*.f64 th (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 th th))) 3)
(pow.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)) 1/3)
(sqrt.f64 (*.f64 1/4 (pow.f64 th 4)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 th) th) -1/2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 -1/2 (.f64 th th)))))
(cbrt.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 th th))))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 th th))))
(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 th th))) 1))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 th th))))

Outputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 th th)) -1/2))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 th th)) -1/2))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (fma.f64 (.f64 -1/2 th) th 1)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 th th) 1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (fma.f64 -1/2 (.f64 th th) 1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (*.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (fma.f64 -1/2 (.f64 th th) 1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))) (.f64 (sqrt.f64 1/2) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a1 2))))
(.f64 (fma.f64 (.f64 -1/2 th) th 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
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(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 th th))) 1))
(.f64 -1/2 (.f64 th th))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 th th))))
(.f64 -1/2 (.f64 th th))

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5%	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
✓	0.51%	(.f64 (cos.f64 th) (.f64 a2 a2))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series3.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	th	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
0.0ms	th	@	0	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
0.0ms	th	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
0.0ms	a2	@	0	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1992×	`add-sqr-sqrt`
1974×	`*-un-lft-identity`
1826×	`add-cube-cbrt`
1798×	`add-cbrt-cube`
212×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	218	44
2	2568	44

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

Inputs
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 a2 a2))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (*.f64 (cos.f64 th) (sqrt.f64 1/2))) a2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (*.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))))))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1028×	`log-prod`
696×	`unswap-sqr`
668×	`+-commutative`
652×	`fma-def`
564×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1938
1	282	1908
2	1111	1814
3	3632	1772
4	6720	1772

Stop Event

1×	node limit

Counts

74 → 74

Calls

Call 1

Inputs
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2))) (.f64 -1/720 (.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (.f64 1/24 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) 1)
(pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 1)
(pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 3)
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 1))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))) 1)
(pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 1)
(pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) a2) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))) 3)
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3) 1/3)
(sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))
(exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))) 1))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))

Outputs
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (.f64 a2 a2) (.f64 -1/2 (.f64 (.f64 a2 a2) (*.f64 th th))))
(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 (.f64 a2 a2) (.f64 th th)) (.f64 1/24 (.f64 (*.f64 a2 a2) (pow.f64 th 4)))))
(fma.f64 a2 a2 (.f64 (.f64 a2 a2) (+.f64 (.f64 -1/2 (.f64 th th)) (*.f64 1/24 (pow.f64 th 4)))))
(.f64 (.f64 a2 a2) (+.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 1/24 (pow.f64 th 4))))
(.f64 (.f64 a2 a2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (fma.f64 -1/2 (.f64 th th) 1)))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (+.f64 (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2))) (.f64 -1/720 (.f64 (pow.f64 th 6) (pow.f64 a2 2))))))
(+.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 (.f64 a2 a2) (.f64 th th)) (fma.f64 1/24 (.f64 (.f64 a2 a2) (pow.f64 th 4)) (.f64 -1/720 (.f64 (*.f64 a2 a2) (pow.f64 th 6))))))
(fma.f64 a2 a2 (fma.f64 -1/2 (.f64 (.f64 a2 a2) (.f64 th th)) (.f64 (.f64 a2 a2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))
(fma.f64 a2 a2 (.f64 (.f64 a2 a2) (+.f64 (.f64 -1/2 (.f64 th th)) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))))))
(.f64 (.f64 a2 a2) (+.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 1/24 (pow.f64 th 4) (.f64 -1/720 (pow.f64 th 6)))))
(.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/24 (pow.f64 th 4) (.f64 -1/720 (pow.f64 th 6))) (fma.f64 -1/2 (.f64 th th) 1)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (pow.f64 a2 2) (cos.f64 th))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (.f64 -1/2 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (.f64 th th))))
(fma.f64 -1/2 (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 1/2)) (.f64 th th))) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 th th) 1)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 (fma.f64 -1/2 (.f64 th th) 1) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (.f64 1/24 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 a2 2) (pow.f64 th 4))))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (fma.f64 -1/2 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (.f64 th th)) (.f64 1/24 (.f64 (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (pow.f64 th 4)))))
(fma.f64 a2 (.f64 a2 (sqrt.f64 1/2)) (fma.f64 -1/2 (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 1/2)) (.f64 th th))) (.f64 (.f64 (.f64 1/24 (*.f64 a2 a2)) (pow.f64 th 4)) (sqrt.f64 1/2))))
(fma.f64 a2 (.f64 a2 (sqrt.f64 1/2)) (.f64 (.f64 (.f64 a2 a2) (sqrt.f64 1/2)) (fma.f64 1/24 (pow.f64 th 4) (.f64 -1/2 (.f64 th th)))))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (fma.f64 -1/2 (*.f64 th th) 1))))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 4)))))))
(fma.f64 (sqrt.f64 1/2) (.f64 a2 a2) (fma.f64 -1/2 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (.f64 th th)) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (pow.f64 th 6))) (.f64 1/24 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (pow.f64 th 4))))))
(fma.f64 a2 (.f64 a2 (sqrt.f64 1/2)) (fma.f64 -1/2 (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 1/2)) (.f64 th th))) (fma.f64 1/24 (.f64 a2 (.f64 (.f64 a2 (sqrt.f64 1/2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (.f64 a2 a2) (.f64 (pow.f64 th 6) (sqrt.f64 1/2)))))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 th th) 1))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (fma.f64 1/24 (pow.f64 th 4) (.f64 -1/720 (pow.f64 th 6))))))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (+.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 1/24 (pow.f64 th 4) (*.f64 -1/720 (pow.f64 th 6))))))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/24 (pow.f64 th 4) (.f64 -1/720 (pow.f64 th 6))) (fma.f64 -1/2 (*.f64 th th) 1))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) 1)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 1)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 2)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 a2 a2))) 3)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3) 1/3)
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4)))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 3))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (*.f64 a2 a2))) 1))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (.f64 a2 a2) (cos.f64 th))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))) 1)
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 1)
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) a2) 2)
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))) 3)
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3) 1/3)
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(sqrt.f64 (.f64 1/2 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))))
(sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 (pow.f64 a2 4) 1/2)))
(sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 a2 4))))
(sqrt.f64 (.f64 1/2 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 a2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))) 3))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))) 1))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2)))))
(.f64 (cos.f64 th) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(.f64 (.f64 a2 a2) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))

eval216.0ms (1.6%)

Compiler: Compiled 10878 to 6943 computations (36.2% saved)

prune107.0ms (0.8%)

Pruning

32 alts after pruning (23 fresh and 9 done)

	Pruned	Kept	Total
New	484	7	491
Fresh	4	16	20
Picked	0	1	1
Done	1	8	9
Total	489	32	521

Error

Counts

521 → 32

Alt Table

Click to see full alt table

Status	Error	Program
	62.74%	(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
✓	1.12%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	37.87%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	66.21%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	42.55%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
✓	62.68%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	45.92%	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	62.51%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	62.65%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	45.86%	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
	62.47%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	62.75%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	62.59%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	70.85%	(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
	62.47%	(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
	45.93%	(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
✓	62.62%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	62.45%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	37.93%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	42.48%	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	62.5%	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	62.63%	(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
	85.75%	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
✓	37.74%	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	66.17%	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
	45.87%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
✓	42.86%	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	42.49%	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	62.44%	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	45.89%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
	42.48%	(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
	62.68%	(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Compiler

Compiled 384 to 294 computations (23.4% saved)

regimes188.0ms (1.4%)

Counts

58 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Outputs
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))

Calls

8 calls:

27.0ms	a1
27.0ms	th
26.0ms	a2
24.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
21.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.72%	1	`a1`
0.72%	1	`a2`
0.72%	1	`th`
0.72%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
0.72%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.72%	1	`(cos.f64 th)`
0.72%	1	`(*.f64 a1 a1)`
0.72%	1	`(*.f64 a2 a2)`

Compiler

Compiled 633 to 344 computations (45.7% saved)

regimes165.0ms (1.2%)

Counts

56 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))

Outputs
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Calls

7 calls:

27.0ms	th
26.0ms	a1
25.0ms	a2
22.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
20.0ms	(cos.f64 th)

Results

Error	Segments	Branch
1.03%	1	`a1`
1.03%	1	`a2`
1.03%	1	`th`
1.03%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.03%	1	`(cos.f64 th)`
1.03%	1	`(*.f64 a1 a1)`
1.03%	1	`(*.f64 a2 a2)`

Compiler

Compiled 579 to 314 computations (45.8% saved)

regimes457.0ms (3.3%)

Counts

51 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

Outputs
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

Calls

7 calls:

275.0ms	(cos.f64 th)
73.0ms	a2
26.0ms	th
24.0ms	a1
19.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
1.04%	1	`a1`
1.04%	1	`a2`
1.04%	1	`th`
1.04%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.04%	1	`(cos.f64 th)`
1.04%	1	`(*.f64 a1 a1)`
1.04%	1	`(*.f64 a2 a2)`

Compiler

Compiled 500 to 277 computations (44.6% saved)

regimes211.0ms (1.5%)

Counts

50 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Outputs
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Calls

7 calls:

68.0ms	a1
39.0ms	(cos.f64 th)
24.0ms	th
24.0ms	a2
18.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
1.12%	1	`a1`
1.12%	1	`a2`
1.12%	1	`th`
1.12%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.12%	1	`(cos.f64 th)`
1.12%	1	`(*.f64 a1 a1)`
1.12%	1	`(*.f64 a2 a2)`

Compiler

Compiled 486 to 272 computations (44% saved)

regimes184.0ms (1.3%)

Counts

49 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Outputs
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Calls

7 calls:

56.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
24.0ms	a1
23.0ms	th
22.0ms	a2
17.0ms	(cos.f64 th)

Results

Error	Segments	Branch
1.24%	1	`a1`
1.24%	1	`a2`
1.24%	1	`th`
1.24%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.24%	1	`(cos.f64 th)`
1.24%	1	`(*.f64 a1 a1)`
1.24%	1	`(*.f64 a2 a2)`

Compiler

Compiled 473 to 268 computations (43.3% saved)

regimes757.0ms (5.5%)

Counts

48 → 4

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) a1) (cos.f64 th)))
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a1)) a1)

Outputs
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Calls

7 calls:

239.0ms	th
129.0ms	a2
109.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
97.0ms	(cos.f64 th)
73.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
9.19%	3	`a1`
9.17%	4	`a2`
11.93%	9	`th`
15.45%	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
15.45%	4	`(cos.f64 th)`
11.83%	3	`(*.f64 a1 a1)`
14.75%	2	`(*.f64 a2 a2)`

Compiler

Compiled 460 to 264 computations (42.6% saved)

bsearch92.0ms (0.7%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
32.0ms	4.435275240599055e-86	8.266203746928573e-85
38.0ms	3.287495813933689e-115	1.0358431179841518e-112
21.0ms	4.335571681536633e-152	1.1915760010677983e-151

Results

37.0ms	75×	body	1024	valid
37.0ms	199×	body	256	valid
13.0ms	46×	body	512	valid

Compiler

Compiled 561 to 420 computations (25.1% saved)

regimes356.0ms (2.6%)

Counts

35 → 4

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))

Outputs
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Calls

6 calls:

145.0ms	th
69.0ms	a2
45.0ms	(cos.f64 th)
45.0ms	a1
24.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
9.19%	3	`a1`
9.17%	4	`a2`
11.96%	9	`th`
15.47%	4	`(cos.f64 th)`
11.83%	3	`(*.f64 a1 a1)`
14.75%	2	`(*.f64 a2 a2)`

Compiler

Compiled 332 to 199 computations (40.1% saved)

bsearch81.0ms (0.6%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	4.435275240599055e-86	8.266203746928573e-85
33.0ms	3.287495813933689e-115	1.0358431179841518e-112
20.0ms	4.335571681536633e-152	1.1915760010677983e-151

Results

33.0ms	211×	body	256	valid
29.0ms	65×	body	1024	valid
14.0ms	44×	body	512	valid

Compiler

Compiled 561 to 420 computations (25.1% saved)

regimes309.0ms (2.2%)

Counts

31 → 4

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))

Outputs
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Calls

6 calls:

120.0ms	th
54.0ms	a2
48.0ms	a1
40.0ms	(cos.f64 th)
20.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
9.19%	3	`a1`
9.18%	4	`a2`
12.01%	9	`th`
15.49%	4	`(cos.f64 th)`
11.83%	3	`(*.f64 a1 a1)`
14.75%	2	`(*.f64 a2 a2)`

Compiler

Compiled 296 to 182 computations (38.5% saved)

bsearch80.0ms (0.6%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	4.435275240599055e-86	8.266203746928573e-85
32.0ms	3.287495813933689e-115	1.0358431179841518e-112
19.0ms	4.335571681536633e-152	1.1915760010677983e-151

Results

37.0ms	228×	body	256	valid
28.0ms	56×	body	1024	valid
11.0ms	36×	body	512	valid

Compiler

Compiled 561 to 420 computations (25.1% saved)

regimes177.0ms (1.3%)

Counts

29 → 3

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Outputs

(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

(*.f64 (*.f64 (+.f64 (*.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)))

(*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Calls

6 calls:

39.0ms	th
39.0ms	a2
28.0ms	a1
23.0ms	(cos.f64 th)
22.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
22.32%	2	`a1`
22.53%	2	`a2`
18.72%	3	`th`
18.72%	2	`(cos.f64 th)`
24.05%	2	`(*.f64 a1 a1)`
23.91%	2	`(*.f64 a2 a2)`

Compiler

Compiled 278 to 172 computations (38.1% saved)

bsearch49.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
24.0ms	1.3225182380887708e-5	0.10746457024292617
24.0ms	-475.03792418117456	-0.21555191585609107

Results

44.0ms	256×	body	256	valid
0.0ms	3×	body	256	infinite

Compiler

Compiled 588 to 436 computations (25.9% saved)

regimes65.0ms (0.5%)

Counts

28 → 1

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)

Outputs
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Calls

5 calls:

14.0ms	th
14.0ms	a2
13.0ms	a1
9.0ms	(*.f64 a2 a2)
8.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
37.74%	1	`a1`
37.74%	1	`a2`
37.74%	1	`th`
37.74%	1	`(*.f64 a1 a1)`
37.74%	1	`(*.f64 a2 a2)`

Compiler

Compiled 264 to 162 computations (38.6% saved)

regimes92.0ms (0.7%)

Counts

15 → 2

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)

Calls

5 calls:

30.0ms	th
23.0ms	a2
15.0ms	a1
10.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
43.14%	2	`a1`
44.1%	2	`a2`
58.59%	3	`th`
45.21%	2	`(*.f64 a1 a1)`
45.95%	2	`(*.f64 a2 a2)`

Compiler

Compiled 126 to 83 computations (34.1% saved)

bsearch33.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
33.0ms	-2.4240066261988876e-136	-1.0214195139647072e-140

Results

13.0ms	83×	body	256	valid
12.0ms	26×	body	1024	valid
6.0ms	19×	body	512	valid

Compiler

Compiled 188 to 148 computations (21.3% saved)

regimes46.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)

Outputs
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))

Calls

5 calls:

14.0ms	th
12.0ms	a2
8.0ms	a1
6.0ms	(*.f64 a2 a2)
5.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
43.15%	2	`a1`
44.12%	2	`a2`
58.62%	3	`th`
45.23%	2	`(*.f64 a1 a1)`
45.97%	2	`(*.f64 a2 a2)`

Compiler

Compiled 51 to 36 computations (29.4% saved)

bsearch32.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
32.0ms	-2.4240066261988876e-136	-1.0214195139647072e-140

Results

14.0ms	88×	body	256	valid
12.0ms	28×	body	1024	valid
3.0ms	12×	body	512	valid

Compiler

Compiled 188 to 148 computations (21.3% saved)

regimes31.0ms (0.2%)

Accuracy

Total -28.0b remaining (-101.1%)

Threshold costs -28b (-101.1%)

Counts

2 → 2

Calls

Call 1

Inputs
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Calls

4 calls:

11.0ms	th
8.0ms	a2
6.0ms	a1
4.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
43.19%	2	`a1`
44.17%	2	`a2`
58.67%	3	`th`
45.27%	2	`(*.f64 a1 a1)`

Compiler

Compiled 33 to 24 computations (27.3% saved)

bsearch33.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
33.0ms	-2.4240066261988876e-136	-1.0214195139647072e-140

Results

13.0ms	30×	body	1024	valid
12.0ms	78×	body	256	valid
6.0ms	20×	body	512	valid

Compiler

Compiled 188 to 148 computations (21.3% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative`
4×	`+-commutative`
2×	`1-exp`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	96	890
1	126	890

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 7783797501194429/117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) a1) a1)) (if (<=.f64 a2 6876220841419621/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 7174182377288279/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 1710076723747261/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 324922229779783/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 8224062725184125/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 810812239707753/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 4332296397063773/43322963970637732180912721627235682866194329302747133987038743447103457934462900359999600095377180907771737671271930809827721216) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 7559138504850089/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 th -7926335344172073/36028797018963968) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (if (<=.f64 th 3602879701896397/144115188075855872) (.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a1 -1636695303948071/13093562431584567480052758787310396608866568184172259157933165472384535185618698219533080369303616628603546736510240284036869026183541572213314110357504) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a1 -6435747806372447/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a1 -5237424972633827/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Outputs
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (.f64 (cos.f64 th) (pow.f64 2 -1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(if (<=.f64 a2 7783797501194429/117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) a1) a1)) (if (<=.f64 a2 6876220841419621/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 7174182377288279/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 7783797501194429/117936325775673167257548580655883402841153788138013763386756446882675755074754651627691460161801836485670886719711370153117830769685149769767544820357271751364043603968) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 6876220841419621/11090678776483259438313656736572334813745748301503266300681918322458485231222502492159897624416558312389564843845614287315896631296) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)) (if (<=.f64 a2 7174182377288279/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 1710076723747261/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 324922229779783/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 8224062725184125/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 1710076723747261/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 324922229779783/5415370496329716522614090203404460358274291162843391748379842930887932241807862544999950011922147613471467208908991351228465152) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)) (if (<=.f64 a2 8224062725184125/34996011596528190789960035633881941845650710894291398982812329702559247987190014771576210832368861184) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 810812239707753/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 4332296397063773/43322963970637732180912721627235682866194329302747133987038743447103457934462900359999600095377180907771737671271930809827721216) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (if (<=.f64 a2 7559138504850089/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 a2 810812239707753/7371020360979572953596786290992712677572111758625860211672277930167234692172165726730716260112614780354430419981960634569864423105321860610471551272329484460252725248) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 4332296397063773/43322963970637732180912721627235682866194329302747133987038743447103457934462900359999600095377180907771737671271930809827721216) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)) (if (<=.f64 a2 7559138504850089/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(if (<=.f64 th -7926335344172073/36028797018963968) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (if (<=.f64 th 3602879701896397/144115188075855872) (.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(if (or (<=.f64 th -7926335344172073/36028797018963968) (not (<=.f64 th 3602879701896397/144115188075855872))) (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (*.f64 th th)) 1))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 1/2))
(if (<=.f64 a1 -1636695303948071/13093562431584567480052758787310396608866568184172259157933165472384535185618698219533080369303616628603546736510240284036869026183541572213314110357504) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a1 -1636695303948071/13093562431584567480052758787310396608866568184172259157933165472384535185618698219533080369303616628603546736510240284036869026183541572213314110357504) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a1 -6435747806372447/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a1 -6435747806372447/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a1 -5237424972633827/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -5237424972633827/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Compiler

Compiled 356 to 242 computations (32% saved)

soundness17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

60×	`fma-def`
50×	`*-commutative`
40×	`associate-/l*`
18×	`associate-/r/`
16×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	30	35
2	56	35
3	79	35
4	106	35
5	124	35
6	142	35
7	147	35
8	149	35

Stop Event

1×

saturated

Compiler

Compiled 35 to 20 computations (42.9% saved)

end129.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 349 to 187 computations (46.4% saved)

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3