Details

analyze365.0ms (2.6%)

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)

sample3.8s (27%)

Results

1.1s	5486×	body	256	valid
1.0s	1859×	body	1024	valid
767.0ms	1664×	body	1024	infinite
312.0ms	830×	body	512	infinite
289.0ms	909×	body	512	valid
263.0ms	1536×	body	256	infinite
2.0ms	2×	body	2048	valid

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)

simplify17.0ms (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)

prune2.0ms (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

0.97%

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.17%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	1.07%	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 31 to 21 computations (32.3% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.23%	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	1%	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 41 to 16 computations (61% saved)

series10.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

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

rewrite128.0ms (0.9%)

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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simplify143.0ms (1%)

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
✓	0.84%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	1.1%	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series6.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite118.0ms (0.8%)

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)))))))

simplify130.0ms (0.9%)

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)))

eval270.0ms (1.9%)

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

prune159.0ms (1.1%)

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
	1.11%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	41.26%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	46.08%	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
▶	43%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
	1.04%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	46.05%	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	1.12%	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	1.07%	(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
	43%	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	41.32%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	1.06%	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	42.98%	(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
▶	46.07%	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	42.95%	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	45.68%	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
	0.72%	(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
▶	1.1%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
▶	0.69%	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 522 to 380 computations (27.2% saved)

localize61.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.23%	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.43%	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
✓	0.52%	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

Compiler

Compiled 48 to 25 computations (47.9% saved)

series21.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
5.0ms	a2	@	0	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
3.0ms	a1	@	0	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
2.0ms	a1	@	0	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
2.0ms	a2	@	0	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
1.0ms	a2	@	-inf	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))

rewrite77.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1096×	`unswap-sqr`
852×	`swap-sqr`
496×	`sqr-pow`
470×	`pow-sqr`
314×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	91
1	285	73
2	3320	73

Stop Event

1×	node limit

Counts

3 → 61

Calls

Call 1

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

Outputs

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

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

simplify160.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1170×	`associate-+r+`
1004×	`+-commutative`
948×	`associate-+l+`
862×	`fma-def`
848×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	9601
1	1357	8655
2	5359	8631

Stop Event

1×	node limit

Counts

145 → 221

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3)))))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))))))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (*.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (*.f64 (sqrt.f64 1/2) a1)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(.f64 -1 (.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (.f64 -1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (*.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (*.f64 (sqrt.f64 1/2) a1)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3)))))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))))))
(.f64 -1 (.f64 (sqrt.f64 1/2) a2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (.f64 -1 (.f64 (sqrt.f64 1/2) a2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 -1 (.f64 (sqrt.f64 1/2) a2))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 -1 (.f64 (sqrt.f64 1/2) a2)))))
(*.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) (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8))) (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
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(pow.f64 (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))) 2)
(pow.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3) 1/3)
(sqrt.f64 (*.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)))))
(cbrt.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3))
(cbrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 3) (.f64 (sqrt.f64 1/2) 1/2)))
(cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (hypot.f64 a1 a2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))
(exp.f64 (log.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))
(log1p.f64 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))
(+.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) -1)
(+.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 (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(+.f64 (.f64 (.f64 a2 a2) (sqrt.f64 1/2)) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (sqrt.f64 1/2)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))
(pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(pow.f64 (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4)) 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 (hypot.f64 a1 a2) 4)))
(log.f64 (exp.f64 (*.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 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3) (pow.f64 (hypot.f64 a1 a2) 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))))
(+.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) -1)
(-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 1)
(/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 1))))
(pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 1)
(pow.f64 (.f64 (sqrt.f64 (cos.f64 th)) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4))) 2)
(pow.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3)))
(expm1.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))
(exp.f64 (log.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))
(log1p.f64 (expm1.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))

Outputs
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(fma.f64 (sqrt.f64 1/2) a2 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1)))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) a2))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3)))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1))) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 3) (pow.f64 a1 4))))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a2) (.f64 a1 a1)) (/.f64 (.f64 -1/8 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4))) (pow.f64 a2 3))))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 3) (pow.f64 a1 4))) (.f64 1/16 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 5) (pow.f64 a1 6)))))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a2) (.f64 a1 a1)) (fma.f64 1/16 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 5) (pow.f64 a1 6))) (/.f64 (.f64 -1/8 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4))) (pow.f64 a2 3)))))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (*.f64 (sqrt.f64 1/2) a1))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (.f64 (sqrt.f64 1/2) a1))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (*.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 a1 3)) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 (sqrt.f64 1/2) a1 (/.f64 (*.f64 -1/8 (pow.f64 a2 4)) (/.f64 (pow.f64 a1 3) (sqrt.f64 1/2)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (fma.f64 (sqrt.f64 1/2) a1 (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 a1 3)) (pow.f64 a2 4)) (fma.f64 (sqrt.f64 1/2) a1 (/.f64 (.f64 (*.f64 1/16 (pow.f64 a2 6)) (sqrt.f64 1/2)) (pow.f64 a1 5)))))
(.f64 -1 (.f64 (sqrt.f64 1/2) a1))
(neg.f64 (*.f64 (sqrt.f64 1/2) a1))
(*.f64 (sqrt.f64 1/2) (neg.f64 a1))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))
(fma.f64 -1 (.f64 (sqrt.f64 1/2) a1) (.f64 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (*.f64 a2 a2))) -1/2))
(-.f64 (/.f64 (.f64 (sqrt.f64 1/2) -1/2) (/.f64 a1 (.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))))
(fma.f64 -1 (.f64 (sqrt.f64 1/2) a1) (fma.f64 1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (.f64 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (*.f64 a2 a2))) -1/2)))
(-.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) -1/2 (/.f64 (.f64 1/8 (sqrt.f64 1/2)) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4)))) (.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 -1 (.f64 (sqrt.f64 1/2) a1)) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (.f64 -1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(fma.f64 -1 (.f64 (sqrt.f64 1/2) a1) (fma.f64 1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (fma.f64 -1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5)) -1/16))))
(-.f64 (fma.f64 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 a1 3)) (pow.f64 a2 4)) 1/8 (fma.f64 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) -1/2 (/.f64 (.f64 (.f64 -1/16 (pow.f64 a2 6)) (sqrt.f64 1/2)) (pow.f64 a1 5)))) (.f64 (sqrt.f64 1/2) a1))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (*.f64 (sqrt.f64 1/2) a1))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (.f64 (sqrt.f64 1/2) a1))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) a1))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (*.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 a1 3)) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) a1)))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 (sqrt.f64 1/2) a1 (/.f64 (*.f64 -1/8 (pow.f64 a2 4)) (/.f64 (pow.f64 a1 3) (sqrt.f64 1/2)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a1 (.f64 a2 a2))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a1 3) (pow.f64 a2 4))) (fma.f64 (sqrt.f64 1/2) a1 (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a1) (.f64 a2 a2)) (fma.f64 -1/8 (.f64 (/.f64 (sqrt.f64 1/2) (pow.f64 a1 3)) (pow.f64 a2 4)) (fma.f64 (sqrt.f64 1/2) a1 (/.f64 (.f64 (*.f64 1/16 (pow.f64 a2 6)) (sqrt.f64 1/2)) (pow.f64 a1 5)))))
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(fma.f64 (sqrt.f64 1/2) a2 (.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1)))))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) a2))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3)))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1))) (.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 3) (pow.f64 a1 4))))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 1/2) a2) (.f64 a1 a1)) (/.f64 (.f64 -1/8 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4))) (pow.f64 a2 3))))
(+.f64 (.f64 (sqrt.f64 1/2) a2) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (.f64 1/16 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))))))
(fma.f64 (sqrt.f64 1/2) a2 (fma.f64 1/2 (/.f64 (sqrt.f64 1/2) (/.f64 a2 (.f64 a1 a1))) (fma.f64 -1/8 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 3) (pow.f64 a1 4))) (.f64 1/16 (/.f64 (sqrt.f64 1/2) (/.f64 (pow.f64 a2 5) (pow.f64 a1 6)))))))
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(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 1/2)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 a1 (.f64 a1 (.f64 a2 a2)))) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 a2 (.f64 a2 (.f64 a1 a1))))) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 1))
(/.f64 (.f64 (+.f64 1 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))) (+.f64 1 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))))))
(/.f64 (expm1.f64 (.f64 2 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))) (+.f64 1 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))) 1))))
(/.f64 (+.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))) 3) -1) (+.f64 (exp.f64 (+.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))) (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))))) (+.f64 1 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))))
(/.f64 (+.f64 -1 (pow.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) 3)) (+.f64 1 (+.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))) (exp.f64 (.f64 2 (log1p.f64 (.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))))))
(pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 1)
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (.f64 (sqrt.f64 (cos.f64 th)) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4))) 2)
(pow.f64 (.f64 (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (.f64 (pow.f64 2 -1/4) (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th)))) 2)
(pow.f64 (cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))) 3)
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 3) 1/3)
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))
(sqrt.f64 (.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)) (pow.f64 (cos.f64 th) 2)))
(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 (hypot.f64 a1 a2) 4)) 1/2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(cbrt.f64 (pow.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) 3))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(expm1.f64 (log1p.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(exp.f64 (log.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))
(log1p.f64 (expm1.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1%	(/.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	a2	@	inf	(/.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	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))

rewrite97.0ms (0.7%)

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))))))))

simplify134.0ms (1%)

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))
(+.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 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.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))
(+.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))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.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))
(+.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))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.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))
(+.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))
(/.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))
(+.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 (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))
(+.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 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(-.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) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.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)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (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))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 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 (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))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 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 (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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) 1))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.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) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 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)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(*.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) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
(*.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) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (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 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) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.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 (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)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.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)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.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 (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 (/.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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 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 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 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 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 a1 a2) 2))))
(/.f64 (.f64 (+.f64 (pow.f64 a1 4) (+.f64 (pow.f64 (.f64 a1 a2) 2) (pow.f64 a2 4))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (*.f64 (sqrt.f64 2) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 (.f64 a1 a2) 2) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(.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 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
✓	0.16%	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
✓	0.8%	(/.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	th	@	0	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
0.0ms	a1	@	inf	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

rewrite101.0ms (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

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

simplify121.0ms (0.9%)

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)))
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(/.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)))
(.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 (exp.f64 (log1p.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) 1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.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 (.f64 a1 a1) (pow.f64 2 -1/2))
(.f64 a1 (.f64 a1 (pow.f64 2 -1/2)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(.f64 1 (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)))
(*.f64 (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (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 a1 (/.f64 (sqrt.f64 2) a1))) (/.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 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 a1 4) 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 a1) (pow.f64 2 -1/2))
(.f64 a1 (.f64 a1 (pow.f64 2 -1/2)))
(.f64 (.f64 a1 (neg.f64 a1)) (/.f64 -1 (sqrt.f64 2)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 a1 4)))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) a1)))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (/.f64 a1 1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (cbrt.f64 (sqrt.f64 2))) (/.f64 a1 (cbrt.f64 2)))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) a1)))
(.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) a1)))
(.f64 (/.f64 -1 (sqrt.f64 2)) (.f64 a1 (neg.f64 a1)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 1) (/.f64 a1 (sqrt.f64 2)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a1 a1)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) a1)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.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 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4))) (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)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4))) (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 (cbrt.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 2) a1)) (sqrt.f64 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (sqrt.f64 a1))) (sqrt.f64 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))) (neg.f64 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a1) 2))) (cbrt.f64 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4)))) (pow.f64 (cbrt.f64 a1) 2))
(*.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (sqrt.f64 2) a1)) (cbrt.f64 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(pow.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) 1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 3)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
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(/.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 (/.f64 a1 (/.f64 (cbrt.f64 2) (cos.f64 th))) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 a1))
(.f64 (cbrt.f64 a1) (/.f64 (.f64 (/.f64 a1 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a1) 2))) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2))))
(/.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 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2))) (pow.f64 2 1/4)) (cbrt.f64 a1))
(.f64 (cbrt.f64 a1) (/.f64 a1 (.f64 (pow.f64 2 1/4) (/.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a1) 2)) (cos.f64 th)))))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) 1) (neg.f64 (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 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (.f64 a1 a1))
(*.f64 (pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2) (cos.f64 th))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (cbrt.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 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (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 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) -1) (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 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (.f64 a1 a1))
(*.f64 (pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2) (cos.f64 th))
(/.f64 (/.f64 (.f64 (.f64 a1 a1) (neg.f64 (cos.f64 th))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (cbrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) 1) (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 (/.f64 (*.f64 a1 a1) (/.f64 1 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (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 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (.f64 a1 a1))
(*.f64 (pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2) (cos.f64 th))
(/.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 (cos.f64 th) (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1))) (.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 a1 (/.f64 a1 (pow.f64 2 1/4))) (cbrt.f64 (sqrt.f64 2))))
(/.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 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (.f64 a1 a1))
(*.f64 (pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2) (cos.f64 th))
(/.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 (cos.f64 th) (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1))) (.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (.f64 a1 (/.f64 a1 (pow.f64 2 1/4))) (sqrt.f64 (cbrt.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) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (cbrt.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) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (cbrt.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 a1 a1) (/.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) (.f64 a1 (/.f64 a1 (cbrt.f64 2)))) (*.f64 (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) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (.f64 a1 a1))
(/.f64 a1 (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a1 (/.f64 (cos.f64 th) (cbrt.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))))
(/.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (cbrt.f64 2))) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 2))))
(.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 2))))
(pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(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)
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(pow.f64 (pow.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(neg.f64 (*.f64 (/.f64 a1 (/.f64 (neg.f64 (sqrt.f64 2)) a1)) (cos.f64 th)))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(neg.f64 (*.f64 (cos.f64 th) (/.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)))
(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)))

localize63.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.12%	(.f64 a2 (.f64 a2 (cos.f64 th)))
✓	0.18%	(*.f64 a2 (cos.f64 th))
✓	0.52%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))

Compiler

Compiled 29 to 12 computations (58.6% saved)

series5.0ms (0%)

Counts

3 → 64

Calls

18 calls:

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

rewrite73.0ms (0.5%)

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))))))))

simplify81.0ms (0.6%)

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)))

localize37.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.23%	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	0.92%	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Compiler

Compiled 51 to 21 computations (58.8% saved)

series4.0ms (0%)

Counts

2 → 60

Calls

15 calls:

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

rewrite100.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`associate-*r/`
864×	`distribute-rgt-in`
818×	`distribute-lft-in`
700×	`associate-*l/`
328×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	320	56
2	4148	56

Stop Event

1×	node limit

Counts

2 → 156

Calls

Call 1

Inputs
(.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 a2 a2) (.f64 a1 a1))))

Outputs

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

simplify181.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1498×	`distribute-lft-in`
1466×	`distribute-rgt-in`
1082×	`associate-/l*`
756×	`associate-r`
754×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	11132
1	1124	10306
2	5017	10306

Stop Event

1×	node limit

Counts

216 → 246

Calls

Call 1

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

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

eval430.0ms (3.1%)

Compiler: Compiled 22746 to 14174 computations (37.7% saved)

prune244.0ms (1.7%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	962	19	981
Fresh	9	4	13
Picked	1	0	1
Done	2	2	4
Total	974	25	999

Error

Counts

999 → 25

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.26%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	69.72%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
	46.08%	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
✓	43%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
▶	64.49%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	64.13%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	64.46%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	64.11%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	41.18%	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	1.07%	(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
	42.98%	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
▶	42.95%	(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
	64.49%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
▶	64.15%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	43%	(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (cos.f64 th))
	41.32%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	1.06%	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	43%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
	46.07%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
	42.99%	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	45.72%	(.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))
	1.1%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
▶	43.02%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	45.74%	(.f64 (cos.f64 th) (.f64 a1 (*.f64 a1 (pow.f64 2 -1/2))))
	45.71%	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Compiler

Compiled 593 to 442 computations (25.5% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.36%	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
✓	0.84%	(.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)

series4.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

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

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(*.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))))))))

simplify100.0ms (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))))
(.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 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 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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(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))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(+.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))))
(.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 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (.f64 a1 a1))))
(.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)))
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(/.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))

localize59.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.33%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.79%	(/.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)

rewrite60.0ms (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)))))))))

simplify63.0ms (0.4%)

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)))

localize26.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.54%	(/.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	@	0	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.0ms	a2	@	inf	(/.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)))))))

simplify57.0ms (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)))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.14%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
✓	0.47%	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))

Compiler

Compiled 28 to 15 computations (46.4% saved)

series8.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
0.0ms	th	@	0	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
0.0ms	th	@	-inf	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))

rewrite68.0ms (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	2569	44

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

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

Outputs

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

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

simplify83.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

902×	`log-prod`
786×	`associate--r+`
698×	`unswap-sqr`
592×	`associate-*r/`
580×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1606
1	253	1606
2	1043	1558
3	3405	1538
4	6668	1538

Stop Event

1×	node limit

Counts

62 → 48

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

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

localize63.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.14%	(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
✓	0.24%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
✓	0.73%	(/.f64 (sqrt.f64 2) a2)

Compiler

Compiled 29 to 19 computations (34.5% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

12 calls:

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

rewrite87.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1566×	`associate-*l/`
1464×	`associate-/l*`
1106×	`*-commutative`
644×	`associate-/r/`
284×	`associate-/l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	229	55
2	2977	55

Stop Event

1×	node limit

Counts

3 → 221

Calls

Call 1

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

Outputs

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

simplify173.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1226×	`times-frac`
1206×	`associate-/l*`
1072×	`distribute-lft-in`
778×	`associate-/r*`
630×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	503	7271
1	1415	7037
2	6825	7037

Stop Event

1×	node limit

Counts

257 → 296

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

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

eval353.0ms (2.5%)

Compiler: Compiled 10415 to 6156 computations (40.9% saved)

prune259.0ms (1.8%)

Pruning

35 alts after pruning (29 fresh and 6 done)

	Pruned	Kept	Total
New	596	14	610
Fresh	3	15	18
Picked	0	1	1
Done	1	5	6
Total	600	35	635

Error

Counts

635 → 35

Alt Table

Click to see full alt table

Status	Error	Program
	64.46%	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
	64.41%	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
✓	41.26%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
▶	69.72%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
	46.08%	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
✓	43%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
✓	64.49%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	64.13%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	64.46%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	64.11%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	64.1%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	64.44%	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
	1.07%	(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
	42.98%	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
✓	42.95%	(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
▶	64.49%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	64.15%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	41.32%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	69.66%	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	64.15%	(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
	48.62%	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
▶	1.06%	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	64.16%	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	86.71%	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
▶	86.71%	(.f64 (sqrt.f64 (.f64 a1 (/.f64 a1 2))) a1)
	41.18%	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	45.68%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
	43%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
▶	46.07%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
	42.99%	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	45.72%	(.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))
	1.1%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	43.02%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	64.42%	(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
	45.71%	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Compiler

Compiled 787 to 594 computations (24.5% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.36%	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓	0.84%	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series2.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite133.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`associate-*r/`
774×	`distribute-rgt-in`
724×	`distribute-lft-in`
634×	`associate-*l/`
302×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	293	48
2	3807	48

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

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

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

904×	`associate-/l*`
818×	`associate-r`
760×	`associate-l`
750×	`distribute-lft-neg-in`
746×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	7407
1	892	6851
2	5470	6685

Stop Event

1×	node limit

Counts

133 → 155

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

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.28%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	0.73%	(/.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	@	0	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	-inf	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	inf	(/.f64 a2 (sqrt.f64 2))
0.0ms	a2	@	inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
0.0ms	a2	@	0	(*.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)))))))))

simplify65.0ms (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)))

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.33%	(.f64 (sqrt.f64 (.f64 a1 (/.f64 a1 2))) a1)
✓	30.11%	(sqrt.f64 (*.f64 a1 (/.f64 a1 2)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite80.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1718×	`add-sqr-sqrt`
1692×	`*-un-lft-identity`
1580×	`add-cube-cbrt`
1556×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	40
1	186	28
2	2212	28

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 a1 (/.f64 a1 2)))
(.f64 (sqrt.f64 (.f64 a1 (/.f64 a1 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 (/.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 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 a1 1/2)) (sqrt.f64 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 a1) (sqrt.f64 (*.f64 a1 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2))) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (/.f64 a1 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 a1 (*.f64 a1 1/2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a1 (*.f64 a1 1/2)) 1/2)))) (#(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 fabs.f64 (/.f64 a1 (sqrt.f64 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 (*.f64 a1 1/2))) 1/2))))) (#(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 pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 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)))))))))

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1378×	`associate-+r+`
1310×	`associate-/l*`
1274×	`associate-+l+`
784×	`*-commutative`
742×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1043
1	206	1031
2	864	1023
3	3727	1023

Stop Event

1×	node limit

Counts

63 → 59

Calls

Call 1

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

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.01%	(.f64 -1/2 (.f64 th th))
✓	0.48%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	13.77%	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series4.0ms (0%)

Counts

3 → 60

Calls

15 calls:

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

rewrite100.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1734×	`associate-*r/`
1696×	`associate-/r*`
1552×	`associate-*l/`
310×	`add-sqr-sqrt`
296×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	313	77
2	3975	77

Stop Event

1×	node limit

Counts

3 → 130

Calls

Call 1

Inputs
(.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 -1/2 (.f64 th th))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 a2))) (-.f64 1 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 a2))) (-.f64 1 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (/.f64 (fma.f64 -1/2 (*.f64 th th) -1) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (/.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) 1)) 2)) (cbrt.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 1/4 (pow.f64 th 4))) (*.f64 a2 a2)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) (*.f64 a2 a2)) (neg.f64 (fma.f64 -1/2 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a2 a2)) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 1/4)) 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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 2 1/4)) (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (cbrt.f64 2)) (/.f64 (*.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) 1) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) 1) (/.f64 (*.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (cbrt.f64 2)) (/.f64 (*.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x 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((#(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 -1/2 (*.f64 th th) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 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 (exp.f64 -1/2) (*.f64 th th)))))) (#(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))))))))

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1534×	`unswap-sqr`
812×	`associate-/l*`
520×	`associate-r`
488×	`associate-l`
448×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	342	7980
1	922	7614
2	4632	7614

Stop Event

1×	node limit

Counts

190 → 217

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.45%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
✓	0.49%	(.f64 (.f64 a1 a1) (cos.f64 th))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series4.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite191.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1988×	`add-sqr-sqrt`
1970×	`*-un-lft-identity`
1822×	`add-cube-cbrt`
1794×	`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 (.f64 a1 a1) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))

Outputs

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

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

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1188×	`associate-/l*`
934×	`log-prod`
724×	`associate-/r*`
630×	`fma-def`
618×	`unswap-sqr`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1934
1	270	1926
2	1084	1852
3	3605	1816
4	6901	1816

Stop Event

1×	node limit

Counts

74 → 71

Calls

Call 1

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

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

eval235.0ms (1.7%)

Compiler: Compiled 11196 to 7029 computations (37.2% saved)

prune136.0ms (1%)

Pruning

40 alts after pruning (31 fresh and 9 done)

	Pruned	Kept	Total
New	559	12	571
Fresh	5	19	24
Picked	1	0	1
Done	1	9	10
Total	566	40	606

Error

Counts

606 → 40

Alt Table

Click to see full alt table

Status	Error	Program
	64.41%	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
✓	41.26%	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
✓	69.72%	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
	46.08%	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	92.04%	(/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2))
✓	43%	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
✓	64.49%	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	64.13%	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	64.46%	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	64.11%	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	64.46%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	64.1%	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	91.57%	(/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 th a2) (*.f64 th a2))))
	64.44%	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
	1.07%	(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
	42.98%	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
✓	42.95%	(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))
✓	64.49%	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	64.15%	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	41.32%	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	69.66%	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	69.73%	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 a1 (*.f64 a1 (sqrt.f64 1/2))))
	64.42%	(.f64 (.f64 (pow.f64 2 -1/2) a2) a2)
	48.62%	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	86.95%	(.f64 (.f64 (sqrt.f64 1/2) (neg.f64 a1)) a1)
✓	1.06%	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	64.52%	(.f64 (.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a2)
	64.16%	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	64.1%	(.f64 (.f64 a1 a1) (sqrt.f64 1/2))
	86.71%	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	69.69%	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
	45.68%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
	43%	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
	42.99%	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	87.01%	(.f64 (sqrt.f64 1/2) (.f64 a1 (neg.f64 a1)))
	86.71%	(*.f64 (fabs.f64 (/.f64 a1 (sqrt.f64 2))) a1)
	45.72%	(.f64 (cos.f64 th) (.f64 (/.f64 a1 (sqrt.f64 2)) a1))
	1.1%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	43.02%	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	45.71%	(.f64 a1 (.f64 (*.f64 a1 (sqrt.f64 1/2)) (cos.f64 th)))

Compiler

Compiled 497 to 377 computations (24.1% saved)

regimes274.0ms (1.9%)

Counts

66 → 1

Calls

Call 1

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

Calls

8 calls:

83.0ms	th
30.0ms	a1
29.0ms	(cos.f64 th)
29.0ms	a2
26.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Results

Error	Segments	Branch
0.69%	1	`a1`
0.69%	1	`a2`
0.69%	1	`th`
0.69%	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
0.69%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.69%	1	`(cos.f64 th)`
0.69%	1	`(*.f64 a1 a1)`
0.69%	1	`(*.f64 a2 a2)`

Compiler

Compiled 727 to 394 computations (45.8% saved)

regimes236.0ms (1.7%)

Counts

64 → 1

Calls

Call 1

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

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

Calls

7 calls:

65.0ms	a2
29.0ms	th
29.0ms	a1
23.0ms	(cos.f64 th)
22.0ms	(/.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 (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 672 to 364 computations (45.8% saved)

regimes289.0ms (2%)

Counts

61 → 1

Calls

Call 1

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

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

Calls

7 calls:

74.0ms	th
68.0ms	a1
28.0ms	a2
23.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
22.0ms	(cos.f64 th)

Results

Error	Segments	Branch
1.06%	1	`a1`
1.06%	1	`a2`
1.06%	1	`th`
1.06%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.06%	1	`(cos.f64 th)`
1.06%	1	`(*.f64 a1 a1)`
1.06%	1	`(*.f64 a2 a2)`

Compiler

Compiled 627 to 338 computations (46.1% saved)

regimes255.0ms (1.8%)

Counts

54 → 1

Calls

Call 1

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

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

Calls

7 calls:

77.0ms	th
28.0ms	a2
26.0ms	a1
20.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
19.0ms	(cos.f64 th)

Results

Error	Segments	Branch
1.1%	1	`a1`
1.1%	1	`a2`
1.1%	1	`th`
1.1%	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
1.1%	1	`(cos.f64 th)`
1.1%	1	`(*.f64 a1 a1)`
1.1%	1	`(*.f64 a2 a2)`

Compiler

Compiled 535 to 307 computations (42.6% saved)

regimes580.0ms (4.1%)

Counts

53 → 2

Calls

Call 1

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

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

Calls

7 calls:

151.0ms	(cos.f64 th)
115.0ms	th
82.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
69.0ms	(*.f64 a2 a2)
68.0ms	a2

Results

Error	Segments	Branch
11.07%	2	`a1`
9.62%	2	`a2`
19.64%	4	`th`
15.79%	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
15.79%	5	`(cos.f64 th)`
15.96%	2	`(*.f64 a1 a1)`
14.32%	6	`(*.f64 a2 a2)`

Compiler

Compiled 522 to 303 computations (42% saved)

bsearch40.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
40.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

17.0ms	93×	body	256	valid
15.0ms	34×	body	1024	valid
6.0ms	17×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes297.0ms (2.1%)

Counts

38 → 2

Calls

Call 1

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

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

Calls

6 calls:

70.0ms	(cos.f64 th)
60.0ms	th
53.0ms	(*.f64 a2 a2)
50.0ms	a2
32.0ms	a1

Results

Error	Segments	Branch
11.09%	2	`a1`
9.69%	2	`a2`
19.74%	4	`th`
15.88%	5	`(cos.f64 th)`
16%	2	`(*.f64 a1 a1)`
14.43%	6	`(*.f64 a2 a2)`

Compiler

Compiled 376 to 229 computations (39.1% saved)

bsearch41.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
40.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

19.0ms	42×	body	1024	valid
14.0ms	85×	body	256	valid
5.0ms	17×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes287.0ms (2%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

6 calls:

63.0ms	(cos.f64 th)
61.0ms	th
52.0ms	a2
49.0ms	(*.f64 a2 a2)
35.0ms	a1

Results

Error	Segments	Branch
11.12%	2	`a1`
9.75%	2	`a2`
19.75%	4	`th`
15.88%	5	`(cos.f64 th)`
16.02%	2	`(*.f64 a1 a1)`
14.45%	6	`(*.f64 a2 a2)`

Compiler

Compiled 367 to 224 computations (39% saved)

bsearch92.0ms (0.7%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
92.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

66.0ms	83×	body	256	valid
18.0ms	41×	body	1024	valid
6.0ms	20×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes300.0ms (2.1%)

Counts

35 → 2

Calls

Call 1

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

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

Calls

6 calls:

80.0ms	th
71.0ms	a1
53.0ms	(*.f64 a1 a1)
33.0ms	(*.f64 a2 a2)
29.0ms	a2

Results

Error	Segments	Branch
28.16%	2	`a1`
26.26%	2	`a2`
24.47%	3	`th`
24.42%	2	`(cos.f64 th)`
30.92%	2	`(*.f64 a1 a1)`
29.91%	4	`(*.f64 a2 a2)`

Compiler

Compiled 349 to 215 computations (38.4% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9983598440812692	0.9993467754918526

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes256.0ms (1.8%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

6 calls:

77.0ms	th
53.0ms	(*.f64 a1 a1)
32.0ms	(*.f64 a2 a2)
30.0ms	a1
28.0ms	a2

Results

Error	Segments	Branch
28.16%	2	`a1`
26.26%	2	`a2`
24.47%	3	`th`
24.42%	2	`(cos.f64 th)`
30.92%	2	`(*.f64 a1 a1)`
29.91%	4	`(*.f64 a2 a2)`

Compiler

Compiled 340 to 210 computations (38.2% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9983598440812692	0.9993467754918526

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes139.0ms (1%)

Counts

33 → 1

Calls

Call 1

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

80.0ms	th
15.0ms	a2
15.0ms	a1
10.0ms	(*.f64 a2 a2)
10.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
41.18%	1	`a1`
41.18%	1	`a2`
41.18%	1	`th`
41.18%	1	`(*.f64 a1 a1)`
41.18%	1	`(*.f64 a2 a2)`

Compiler

Compiled 326 to 200 computations (38.7% saved)

regimes136.0ms (1%)

Counts

17 → 2

Calls

Call 1

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

Calls

5 calls:

41.0ms	(*.f64 a2 a2)
32.0ms	th
24.0ms	a2
20.0ms	a1
15.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
46.21%	2	`a1`
45.92%	2	`a2`
55.6%	4	`th`
48.4%	2	`(*.f64 a1 a1)`
47.93%	4	`(*.f64 a2 a2)`

Compiler

Compiled 143 to 95 computations (33.6% saved)

bsearch41.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
41.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

16.0ms	94×	body	256	valid
16.0ms	34×	body	1024	valid
7.0ms	16×	body	512	valid

Compiler

Compiled 217 to 173 computations (20.3% saved)

regimes120.0ms (0.9%)

Counts

7 → 2

Calls

Call 1

Inputs
(.f64 (.f64 a1 a1) (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))

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

Calls

5 calls:

67.0ms	(*.f64 a2 a2)
18.0ms	th
14.0ms	a2
9.0ms	a1
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
46.24%	2	`a1`
45.95%	2	`a2`
55.61%	4	`th`
48.41%	2	`(*.f64 a1 a1)`
47.98%	4	`(*.f64 a2 a2)`

Compiler

Compiled 69 to 47 computations (31.9% saved)

bsearch76.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
76.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

53.0ms	92×	body	256	valid
15.0ms	33×	body	1024	valid
6.0ms	19×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

regimes42.0ms (0.3%)

Counts

4 → 2

Calls

Call 1

Inputs
(.f64 (.f64 a1 a1) (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))

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

Calls

4 calls:

13.0ms	th
12.0ms	a2
8.0ms	a1
8.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
46.27%	2	`a1`
45.98%	2	`a2`
55.63%	4	`th`
48.44%	2	`(*.f64 a1 a1)`

Compiler

Compiled 45 to 32 computations (28.9% saved)

bsearch40.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
40.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

16.0ms	101×	body	256	valid
13.0ms	29×	body	1024	valid
9.0ms	14×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

regimes42.0ms (0.3%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

4 calls:

13.0ms	th
10.0ms	(*.f64 a1 a1)
10.0ms	a2
7.0ms	a1

Results

Error	Segments	Branch
46.27%	2	`a1`
46.01%	2	`a2`
55.63%	4	`th`
48.44%	2	`(*.f64 a1 a1)`

Compiler

Compiled 39 to 28 computations (28.2% saved)

bsearch44.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
44.0ms	2.127388961929554e-158	4.5821855755987404e-150

Results

21.0ms	40×	body	1024	valid
15.0ms	89×	body	256	valid
5.0ms	15×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

regimes18.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

6.0ms	a2
5.0ms	(*.f64 a1 a1)
3.0ms	a1
3.0ms	th

Results

Error	Segments	Branch
64.1%	1	`a1`
64.1%	1	`a2`
64.1%	1	`th`
64.1%	1	`(*.f64 a1 a1)`

Compiler

Compiled 33 to 24 computations (27.3% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
4×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	715
1	97	715

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(if (<=.f64 a2 4054061198538765/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 (.f64 a1 (sqrt.f64 1/2)) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 4127771402148561/3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742230126362624) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 a2 (.f64 a2 (pow.f64 2 -1/2))))
(if (<=.f64 a2 7371020360979573/1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a2 6191657103222841/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (.f64 a1 a1) (sqrt.f64 1/2))

Outputs
(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(.f64 (cos.f64 th) (+.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 a2 4054061198538765/921377545122446619199598286374089084696513969828232526459034741270904336521520715841339532514076847544303802497745079321233052888165232576308943909041185557531590656) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 (.f64 a1 (sqrt.f64 1/2)) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 (cos.f64 th) (.f64 a1 (sqrt.f64 1/2)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8998192055486251/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 4127771402148561/3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742230126362624) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 a2 (.f64 a2 (pow.f64 2 -1/2))))
(if (<=.f64 a2 7371020360979573/1842755090244893238399196572748178169393027939656465052918069482541808673043041431682679065028153695088607604995490158642466105776330465152617887818082371115063181312) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a2 6191657103222841/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 6191657103222841/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 2073099476525505/460688772561223309599799143187044542348256984914116263229517370635452168260760357920669766257038423772151901248872539660616526444082616288154471954520592778765795328) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (.f64 a1 a1) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))

Compiler

Compiled 296 to 207 computations (30.1% saved)

soundness20.0ms (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 73 to 33 computations (54.8% saved)

end125.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 288 to 163 computations (43.4% 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