Details

analyze323.0ms (1.9%)

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)

sample3.3s (19.3%)

Results

937.0ms	5511×	body	256	valid
866.0ms	1820×	body	1024	valid
695.0ms	1600×	body	1024	infinite
271.0ms	922×	body	512	valid
268.0ms	776×	body	512	infinite
261.0ms	1548×	body	256	infinite
2.0ms	3×	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)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 4

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune3.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Error

0.3b

Counts

5 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Status

Error

Program

▶

0.4b

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

▶

0.4b

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

▶

0.4b

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

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 41 to 16 computations (61% saved)

series11.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

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

rewrite82.0ms (0.5%)

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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simplify110.0ms (0.6%)

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)))

localize36.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series4.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite99.0ms (0.6%)

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)))))))

simplify108.0ms (0.6%)

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)))

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series8.0ms (0%)

Counts

3 → 84

Calls

21 calls:

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

rewrite115.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1472×	`associate-/r*`
1030×	`associate-/l*`
644×	`distribute-lft-in`
342×	`associate-+l+`
330×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	93
1	321	89
2	4376	89

Stop Event

1×	node limit

Counts

3 → 299

Calls

Call 1

Inputs

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

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

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

Outputs

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(cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2) (*.f64 a1 (*.f64 (/.f64 a1 (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 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 (*.f64 (/.f64 a1 (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 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))) (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))) (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a1 4))) (cbrt.f64 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))) (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4))) (cbrt.f64 (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))) (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)) a1 (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)) a2 (*.f64 a1 (*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))))))))

simplify160.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1740×	`associate-/l*`
1664×	`associate-/l/`
1018×	`associate-r`
1006×	`associate-/r/`
884×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	822	21803
1	2392	21803

Stop Event

1×	node limit

Counts

383 → 544

Calls

Call 1

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

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

eval697.0ms (4%)

Compiler: Compiled 32790 to 18801 computations (42.7% saved)

prune469.0ms (2.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	1218	18	1236
Fresh	0	0	0
Picked	1	0	1
Done	2	0	2
Total	1221	18	1239

Error

Counts

1239 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	24.9b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	34.2b	(/.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)))
▶	27.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	28.0b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	28.1b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (/.f64 (cos.f64 th) (.f64 (pow.f64 2 1/4) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))))
	24.9b	(+.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 a1 (/.f64 a1 (sqrt.f64 2))))
	0.5b	(*.f64 (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2) (cos.f64 th))
▶	0.5b	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	27.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
▶	28.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	25.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	27.3b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	28.0b	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 572 to 410 computations (28.3% saved)

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.3b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

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

rewrite101.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	299	48
2	4065	48

Stop Event

1×	node limit

Counts

2 → 112

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 a2 a1) (*.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 2)) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 -1 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (*.f64 (/.f64 (hypot.f64 a2 a1) 1) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) 1) (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (cos.f64 th)) (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1) (*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) 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simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1540×	`distribute-lft-in`
1522×	`distribute-rgt-in`
550×	`associate-r`
482×	`*-commutative`
476×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6050
1	1009	5722
2	4853	5718

Stop Event

1×	node limit

Counts

152 → 186

Calls

Call 1

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

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

localize22.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.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))

rewrite62.0ms (0.4%)

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))))))))

simplify84.0ms (0.5%)

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))
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(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))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (.f64 a2 a2))
✓	0.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series2.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite72.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1490×	`associate-/r*`
1376×	`associate-/l*`
1064×	`*-commutative`
892×	`associate-*r/`
618×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	224	44
2	2875	44

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

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

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

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1648×	`unswap-sqr`
982×	`associate-/r*`
786×	`associate-/l/`
716×	`associate-/r/`
488×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4350
1	661	4252
2	2487	4214

Stop Event

1×	node limit

Counts

134 → 145

Calls

Call 1

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

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

localize25.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.6b	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
✓	0.7b	(/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4))

Compiler

Compiled 60 to 33 computations (45% saved)

series135.0ms (0.8%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
68.0ms	th	@	inf	(/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4))
47.0ms	th	@	inf	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
9.0ms	th	@	inf	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
3.0ms	th	@	0	(/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4))
2.0ms	a1	@	0	(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (pow.f64 2 1/4)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

rewrite95.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`distribute-rgt-in`
880×	`distribute-lft-in`
632×	`associate-/r/`
604×	`associate-/l/`
356×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	95
1	352	65
2	4915	65

Stop Event

1×	node limit

Counts

3 → 173

Calls

Call 1

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

Outputs

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

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1300×	`associate-r`
1258×	`associate-l`
1222×	`times-frac`
1078×	`associate-/l*`
870×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	503	10817
1	1569	10117

Stop Event

1×	node limit

Counts

233 → 296

Calls

Call 1

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

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

eval343.0ms (2%)

Compiler: Compiled 18369 to 10889 computations (40.7% saved)

prune236.0ms (1.4%)

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	898	22	920
Fresh	11	2	13
Picked	1	0	1
Done	0	4	4
Total	910	28	938

Error

Counts

938 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	25.0b	(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
✓	0.4b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	24.9b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	42.7b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	27.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	43.8b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
	39.9b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.0b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	39.7b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	39.9b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.0b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	39.7b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	25.0b	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	27.3b	(.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
▶	0.4b	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	28.0b	(.f64 (/.f64 (.f64 (/.f64 a1 (pow.f64 2 1/4)) a1) (pow.f64 2 1/4)) (cos.f64 th))
	27.3b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a2)) (/.f64 a2 (pow.f64 2 1/4)))
✓	28.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	27.3b	(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cos.f64 th) a2))
	39.9b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
▶	39.7b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
▶	39.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
▶	28.0b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))
	27.3b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	28.0b	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
	27.3b	(.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))
	27.3b	(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
	28.0b	(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))

Compiler

Compiled 651 to 496 computations (23.8% saved)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	0.4b	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

Compiler

Compiled 49 to 16 computations (67.3% saved)

series2.0ms (0%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	th	@	-inf	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	th	@	0	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
0.0ms	th	@	0	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	a2	@	inf	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	a1	@	inf	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite92.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`associate-*r/`
864×	`distribute-rgt-in`
814×	`distribute-lft-in`
682×	`associate-*l/`
308×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	301	58
2	3943	58

Stop Event

1×	node limit

Counts

2 → 156

Calls

Call 1

Inputs
(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Outputs

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

simplify135.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1662×	`distribute-lft-in`
1624×	`distribute-rgt-in`
1062×	`associate-/l*`
852×	`associate-r`
818×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	435	12046
1	1184	11382
2	5240	11382

Stop Event

1×	node limit

Counts

228 → 266

Calls

Call 1

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

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

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.4b	(/.f64 a1 (sqrt.f64 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite55.0ms (0.3%)

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)))))))))

simplify62.0ms (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)))

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
✓	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 23 to 17 computations (26.1% saved)

series0.0ms (0%)

Counts

2 → 12

Calls

3 calls:

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

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1668×	`add-sqr-sqrt`
1646×	`*-un-lft-identity`
1532×	`add-cube-cbrt`
1512×	`add-cbrt-cube`
180×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	198	22
2	2302	22

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

Outputs

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

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

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-r`
916×	`associate-l`
810×	`associate-+r+`
800×	`associate-+l+`
398×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	871
1	237	851
2	892	845
3	4098	845

Stop Event

1×	node limit

Counts

59 → 62

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

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
✓	0.1b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	0.4b	(/.f64 (sqrt.f64 2) a1)

Compiler

Compiled 29 to 19 computations (34.5% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

12 calls:

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

rewrite80.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1522×	`associate-*l/`
1416×	`associate-/l*`
1108×	`*-commutative`
602×	`associate-/r/`
268×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	229	55
2	2975	55

Stop Event

1×	node limit

Counts

3 → 209

Calls

Call 1

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

Outputs

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

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1064×	`distribute-rgt-in`
1048×	`distribute-lft-in`
1014×	`associate-/l*`
886×	`times-frac`
628×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	477	6631
1	1336	6409
2	6106	6409

Stop Event

1×	node limit

Counts

245 → 275

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

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
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(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(cbrt.f64 (.f64 (pow.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) (pow.f64 (cos.f64 th) 3)))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
✓	0.3b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

series4.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1048×	`*-commutative`
912×	`sqrt-prod`
864×	`unswap-sqr`
630×	`swap-sqr`
412×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	245	42
2	2877	42

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

Outputs

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

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1566×	`associate-/r*`
934×	`unswap-sqr`
732×	`fma-def`
658×	`*-commutative`
632×	`associate-/l/`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	2150
1	376	2098
2	1377	2026
3	4973	1986

Stop Event

1×	node limit

Counts

72 → 81

Calls

Call 1

Inputs
(*.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 (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)))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (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))) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(*.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 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))))) -1)
(-.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))))) 1)
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))))) (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1)))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))))) (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1)))))) (+.f64 1 (.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))))) 1))))
(pow.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))) 1)
(pow.f64 (.f64 a1 (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)
(pow.f64 (cbrt.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1)))) 3)
(pow.f64 (.f64 (pow.f64 a1 4) (.f64 (pow.f64 (cos.f64 th) 2) 1/2)) 1/2)
(pow.f64 (pow.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 a1 4) (.f64 (pow.f64 (cos.f64 th) 2) 1/2)))
(fabs.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 a1) a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))))))
(cbrt.f64 (pow.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1))) 3))
(cbrt.f64 (.f64 (pow.f64 a1 6) (pow.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))
(expm1.f64 (log1p.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1)))))
(exp.f64 (log.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1)))))
(log1p.f64 (expm1.f64 (.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1)))))
(+.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) -1)
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1)
(/.f64 (-.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1) (+.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1))
(/.f64 (-.f64 (pow.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3) 1) (+.f64 (.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))))) (+.f64 1 (.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 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) 1/2)
(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))
(fabs.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(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 (pow.f64 (cos.f64 th) 3) (sqrt.f64 1/8)))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.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 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 th th))) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (.f64 th a1) (.f64 th a1)) -1/2)))
(.f64 (.f64 a1 a1) (.f64 (+.f64 (.f64 -1/2 (*.f64 th th)) 1) (sqrt.f64 1/2)))
(.f64 (.f64 a1 a1) (.f64 (+.f64 1 (.f64 -1/2 (*.f64 th th))) (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 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 th th))) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (pow.f64 th 4)))) (fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (.f64 th a1) (*.f64 th a1)) -1/2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (.f64 th th)) (*.f64 1/24 (pow.f64 th 4))))))
(.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (.f64 th th)) (+.f64 1 (.f64 1/24 (pow.f64 th 4))))))
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(*.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))

eval319.0ms (1.9%)

Compiler: Compiled 14158 to 8200 computations (42.1% saved)

prune223.0ms (1.3%)

Pruning

32 alts after pruning (25 fresh and 7 done)

	Pruned	Kept	Total
New	743	10	753
Fresh	4	15	19
Picked	1	0	1
Done	1	7	8
Total	749	32	781

Error

Counts

781 → 32

Alt Table

Click to see full alt table

Status	Error	Program
	39.8b	(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
✓	0.4b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	24.9b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
▶	42.7b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	27.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	43.8b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
	39.9b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.0b	(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
	39.7b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	39.9b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.0b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	39.7b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	39.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
▶	25.0b	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	27.3b	(.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	28.7b	(.f64 (pow.f64 1/4 1/4) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 -1/2 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th)))))
✓	0.4b	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	27.3b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a2)) (/.f64 a2 (pow.f64 2 1/4)))
✓	28.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
▶	27.3b	(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cos.f64 th) a2))
	39.9b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	39.7b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	39.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	42.6b	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (*.f64 a1 a1))
	39.8b	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	53.9b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
▶	53.9b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	28.0b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
▶	39.8b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	27.3b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	27.3b	(.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))
	27.3b	(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))

Compiler

Compiled 726 to 542 computations (25.3% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Compiler

Compiled 34 to 15 computations (55.9% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite135.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`*-commutative`
976×	`unswap-sqr`
576×	`swap-sqr`
558×	`associate-*r/`
478×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	242	23
2	3162	23

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1514×	`associate-/l*`
1374×	`associate-+r+`
968×	`associate-/r*`
852×	`*-commutative`
566×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3427
1	510	3253
2	2203	3217
3	7588	3217

Stop Event

1×	node limit

Counts

75 → 87

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

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

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite73.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1368×	`add-sqr-sqrt`
1350×	`*-un-lft-identity`
1252×	`add-cube-cbrt`
1236×	`add-cbrt-cube`
1224×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	158	17
2	1802	17

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1474×	`distribute-rgt-in`
1446×	`distribute-lft-in`
1208×	`log-prod`
754×	`associate-r`
696×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	391
1	96	391
2	364	391
3	2000	391

Stop Event

1×	node limit

Counts

23 → 14

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 a1 (/.f64 2 a1))
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
✓	20.2b	(sqrt.f64 (/.f64 a1 (/.f64 2 a1)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1900×	`add-sqr-sqrt`
1872×	`*-un-lft-identity`
1754×	`add-cube-cbrt`
1732×	`add-cbrt-cube`
182×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	53
1	191	53
2	2447	53

Stop Event

1×	node limit

Counts

3 → 93

Calls

Call 1

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

Outputs

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

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

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

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1466×	`associate-*r/`
1126×	`associate-/l*`
840×	`*-commutative`
696×	`associate-*l/`
660×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2497
1	472	2399
2	1974	2385

Stop Event

1×	node limit

Counts

129 → 125

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

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

localize47.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	9.8b	(.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

2 → 48

Calls

12 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	a2	@	0	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
0.0ms	a2	@	inf	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2))

rewrite83.0ms (0.5%)

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	64
1	313	64
2	3975	64

Stop Event

1×	node limit

Counts

2 → 113

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))

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 egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.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 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2))) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) a2)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (-.f64 1 (*.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 a2 a2) (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1))) (neg.f64 (fma.f64 -1/2 (*.f64 th th) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))))))) (#(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 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))))))))) (#(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 (*.f64 th th) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) 1) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2)) 1) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) a2) a2) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) 1) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.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))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2)) 1) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.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 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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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simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1274×	`unswap-sqr`
804×	`associate-/l*`
708×	`fma-def`
494×	`associate-r`
466×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	7411
1	856	7097
2	4365	7011

Stop Event

1×	node limit

Counts

161 → 198

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 (.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)))))

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) a2)
✓	0.2b	(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cos.f64 th) a2))
✓	0.4b	(/.f64 a2 (sqrt.f64 2))

Compiler

Compiled 27 to 15 computations (44.4% saved)

series3.0ms (0%)

Counts

3 → 32

Calls

15 calls:

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

rewrite100.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1108×	`*-commutative`
944×	`associate-*r/`
858×	`unswap-sqr`
848×	`associate-/r*`
764×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	225	49
2	2812	49

Stop Event

1×	node limit

Counts

3 → 184

Calls

Call 1

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

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

simplify117.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1498×	`associate-/l*`
1322×	`distribute-lft-in`
750×	`associate-/l/`
720×	`associate-l`
652×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	486	6710
1	1298	6582
2	6832	6582

Stop Event

1×	node limit

Counts

216 → 264

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

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

eval241.0ms (1.4%)

Compiler: Compiled 12019 to 7697 computations (36% saved)

prune168.0ms (1%)

Pruning

37 alts after pruning (26 fresh and 11 done)

	Pruned	Kept	Total
New	679	9	688
Fresh	3	17	20
Picked	0	1	1
Done	1	10	11
Total	683	37	720

Error

Counts

720 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	39.8b	(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
	39.8b	(pow.f64 (*.f64 a1 (pow.f64 1/2 1/4)) 2)
✓	0.4b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
✓	24.9b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
✓	42.7b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
	55.4b	(/.f64 (.f64 (.f64 (.f64 a2 (.f64 a2 -1/2)) th) th) (sqrt.f64 2))
✓	27.3b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	58.0b	(/.f64 (.f64 a2 (.f64 a2 (.f64 th (.f64 -1/2 th)))) (sqrt.f64 2))
	39.9b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.0b	(/.f64 (*.f64 a1 (cos.f64 th)) (/.f64 (sqrt.f64 2) a1))
	39.7b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	25.1b	(/.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))
	39.9b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.0b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	39.7b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	27.3b	(.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	28.7b	(.f64 (pow.f64 1/4 1/4) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 -1/2 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th)))))
✓	0.4b	(.f64 (pow.f64 1/4 1/4) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	28.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	27.3b	(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cos.f64 th) a2))
	39.9b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	39.7b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	53.9b	(.f64 (/.f64 1 (sqrt.f64 (/.f64 2 (.f64 a1 a1)))) a1)
✓	39.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	42.6b	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (*.f64 a1 a1))
	54.0b	(.f64 (.f64 (sqrt.f64 1/2) (neg.f64 a1)) a1)
	39.8b	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	53.9b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
✓	53.9b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	25.0b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	39.9b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
	28.0b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
	54.0b	(.f64 (sqrt.f64 1/2) (.f64 a1 (neg.f64 a1)))
✓	39.8b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	27.3b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	27.3b	(.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))
	27.3b	(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))

Compiler

Compiled 457 to 343 computations (24.9% saved)

regimes229.0ms (1.3%)

Counts

62 → 1

Calls

Call 1

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

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

Calls

8 calls:

43.0ms	(cos.f64 th)
29.0ms	a1
28.0ms	a2
27.0ms	th
25.0ms	(+.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
0.4b	1	`a1`
0.4b	1	`a2`
0.4b	1	`th`
0.4b	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
0.4b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.4b	1	`(cos.f64 th)`
0.4b	1	`(*.f64 a1 a1)`
0.4b	1	`(*.f64 a2 a2)`

Compiler

Compiled 732 to 400 computations (45.4% saved)

regimes140.0ms (0.8%)

Counts

47 → 1

Calls

Call 1

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

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

Calls

7 calls:

23.0ms	a2
22.0ms	a1
22.0ms	th
18.0ms	(cos.f64 th)
17.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.4b	1	`a1`
0.4b	1	`a2`
0.4b	1	`th`
0.4b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.4b	1	`(cos.f64 th)`
0.4b	1	`(*.f64 a1 a1)`
0.4b	1	`(*.f64 a2 a2)`

Compiler

Compiled 484 to 271 computations (44% saved)

regimes738.0ms (4.3%)

Counts

45 → 4

Calls

Call 1

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

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

Calls

7 calls:

175.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
138.0ms	a1
107.0ms	a2
107.0ms	th
90.0ms	(cos.f64 th)

Results

Error	Segments	Branch
6.5b	4	`a1`
6.3b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.5b	2	`(*.f64 a1 a1)`
8.4b	8	`(*.f64 a2 a2)`

Compiler

Compiled 458 to 258 computations (43.7% saved)

bsearch97.0ms (0.6%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
48.0ms	1.3330555992957207e-80	2.7934226473478403e-80
12.0ms	4.477055849904239e-94	6.329035678272607e-94
36.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

57.0ms	65×	body	1024	valid
24.0ms	151×	body	256	valid
12.0ms	40×	body	512	valid

Compiler

Compiled 449 to 345 computations (23.2% saved)

regimes780.0ms (4.5%)

Counts

44 → 4

Calls

Call 1

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

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

Calls

7 calls:

181.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
131.0ms	th
117.0ms	a2
114.0ms	(cos.f64 th)
100.0ms	a1

Results

Error	Segments	Branch
6.5b	4	`a1`
6.4b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.5b	2	`(*.f64 a1 a1)`
8.4b	8	`(*.f64 a2 a2)`

Compiler

Compiled 448 to 254 computations (43.3% saved)

bsearch72.0ms (0.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
22.0ms	1.3330555992957207e-80	2.7934226473478403e-80
14.0ms	4.477055849904239e-94	6.329035678272607e-94
35.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

29.0ms	157×	body	256	valid
27.0ms	56×	body	1024	valid
12.0ms	43×	body	512	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes651.0ms (3.8%)

Counts

41 → 4

Calls

Call 1

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

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

Calls

7 calls:

120.0ms	a2
117.0ms	th
108.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
90.0ms	a1
82.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.5b	4	`a1`
6.4b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.5b	2	`(*.f64 a1 a1)`
8.5b	8	`(*.f64 a2 a2)`

Compiler

Compiled 419 to 240 computations (42.7% saved)

bsearch76.0ms (0.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
20.0ms	1.3330555992957207e-80	2.7934226473478403e-80
12.0ms	4.477055849904239e-94	6.329035678272607e-94
44.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

26.0ms	44×	body	512	valid
26.0ms	165×	body	256	valid
21.0ms	47×	body	1024	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes574.0ms (3.3%)

Counts

33 → 4

Calls

Call 1

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

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

Calls

7 calls:

127.0ms	th
104.0ms	(*.f64 a2 a2)
93.0ms	(cos.f64 th)
89.0ms	a2
69.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
6.6b	4	`a1`
6.4b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.5b	2	`(*.f64 a1 a1)`
8.5b	8	`(*.f64 a2 a2)`

Compiler

Compiled 347 to 206 computations (40.6% saved)

bsearch160.0ms (0.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
19.0ms	1.3330555992957207e-80	2.7934226473478403e-80
14.0ms	4.477055849904239e-94	6.329035678272607e-94
126.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

76.0ms	55×	body	1024	valid
55.0ms	48×	body	512	valid
23.0ms	153×	body	256	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes602.0ms (3.5%)

Counts

32 → 4

Calls

Call 1

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

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

Calls

7 calls:

114.0ms	(cos.f64 th)
103.0ms	a2
101.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
95.0ms	(*.f64 a2 a2)
83.0ms	th

Results

Error	Segments	Branch
6.6b	4	`a1`
6.4b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.5b	2	`(*.f64 a1 a1)`
8.5b	8	`(*.f64 a2 a2)`

Compiler

Compiled 338 to 201 computations (40.5% saved)

bsearch71.0ms (0.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
21.0ms	1.3330555992957207e-80	2.7934226473478403e-80
14.0ms	4.477055849904239e-94	6.329035678272607e-94
36.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

35.0ms	167×	body	256	valid
20.0ms	45×	body	1024	valid
13.0ms	44×	body	512	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes610.0ms (3.5%)

Counts

31 → 4

Calls

Call 1

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

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

Calls

7 calls:

118.0ms	th
105.0ms	(cos.f64 th)
104.0ms	(*.f64 a2 a2)
98.0ms	a1
91.0ms	a2

Results

Error	Segments	Branch
6.6b	4	`a1`
6.4b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.6b	2	`(*.f64 a1 a1)`
8.6b	8	`(*.f64 a2 a2)`

Compiler

Compiled 329 to 196 computations (40.4% saved)

bsearch76.0ms (0.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
23.0ms	1.3330555992957207e-80	2.7934226473478403e-80
14.0ms	4.477055849904239e-94	6.329035678272607e-94
38.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

31.0ms	163×	body	256	valid
28.0ms	61×	body	1024	valid
9.0ms	32×	body	512	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes567.0ms (3.3%)

Counts

30 → 4

Calls

Call 1

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

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

Calls

7 calls:

108.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
99.0ms	a2
95.0ms	(cos.f64 th)
89.0ms	(*.f64 a2 a2)
75.0ms	a1

Results

Error	Segments	Branch
6.6b	4	`a1`
6.5b	4	`a2`
10.6b	5	`th`
10.1b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
10.1b	6	`(cos.f64 th)`
10.6b	2	`(*.f64 a1 a1)`
8.6b	8	`(*.f64 a2 a2)`

Compiler

Compiled 320 to 191 computations (40.3% saved)

bsearch74.0ms (0.4%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
21.0ms	1.3330555992957207e-80	2.7934226473478403e-80
12.0ms	4.477055849904239e-94	6.329035678272607e-94
41.0ms	1.275770365127035e-140	2.776483926705802e-137

Results

30.0ms	158×	body	256	valid
29.0ms	59×	body	1024	valid
11.0ms	39×	body	512	valid

Compiler

Compiled 444 to 340 computations (23.4% saved)

regimes583.0ms (3.4%)

Counts

29 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

7 calls:

376.0ms	(*.f64 a1 a1)
77.0ms	th
38.0ms	a1
26.0ms	a2
21.0ms	(cos.f64 th)

Results

Error	Segments	Branch
16.7b	2	`a1`
16.6b	2	`a2`
14.0b	3	`th`
14.2b	2	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
14.2b	2	`(cos.f64 th)`
18.0b	2	`(*.f64 a1 a1)`
18.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 311 to 186 computations (40.2% saved)

bsearch53.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
25.0ms	85079137.47502549	103012281404.28429
29.0ms	-5.783124891118443e+23	-56435484364626.44

Results

48.0ms

288×

body

256

valid

Compiler

Compiled 784 to 488 computations (37.8% saved)

regimes109.0ms (0.6%)

Counts

28 → 1

Calls

Call 1

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

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

Calls

5 calls:

50.0ms	(*.f64 a2 a2)
16.0ms	a1
14.0ms	th
13.0ms	a2
8.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
24.9b	1	`a1`
24.9b	1	`a2`
24.9b	1	`th`
24.9b	1	`(*.f64 a1 a1)`
24.9b	1	`(*.f64 a2 a2)`

Compiler

Compiled 289 to 169 computations (41.5% saved)

regimes78.0ms (0.5%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

5 calls:

41.0ms	(*.f64 a2 a2)
9.0ms	a1
9.0ms	th
9.0ms	a2
5.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
25.0b	1	`a1`
25.0b	1	`a2`
25.0b	1	`th`
25.0b	1	`(*.f64 a1 a1)`
25.0b	1	`(*.f64 a2 a2)`

Compiler

Compiled 151 to 95 computations (37.1% saved)

regimes116.0ms (0.7%)

Counts

14 → 4

Calls

Call 1

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

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

Calls

5 calls:

32.0ms	a1
32.0ms	th
23.0ms	a2
13.0ms	(*.f64 a2 a2)
13.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.8b	4	`a1`
28.2b	2	`a2`
36.0b	4	`th`
30.3b	2	`(*.f64 a1 a1)`
31.1b	2	`(*.f64 a2 a2)`

Compiler

Compiled 121 to 78 computations (35.5% saved)

bsearch85.0ms (0.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
41.0ms	-1.3457237152912733e-136	-2.2827810051209311e-144
8.0ms	-5.642449152827116e-86	-5.1255777530406294e-86
35.0ms	-4.8678311562813576e-74	-6.662044007232661e-77

Results

35.0ms	198×	body	256	valid
28.0ms	67×	body	1024	valid
17.0ms	39×	body	512	valid

Compiler

Compiled 408 to 324 computations (20.6% saved)

regimes70.0ms (0.4%)

Counts

5 → 4

Calls

Call 1

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

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

Calls

5 calls:

19.0ms	a1
18.0ms	th
14.0ms	a2
9.0ms	(*.f64 a2 a2)
8.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.8b	4	`a1`
28.2b	2	`a2`
36.0b	4	`th`
30.3b	2	`(*.f64 a1 a1)`
31.1b	2	`(*.f64 a2 a2)`

Compiler

Compiled 57 to 40 computations (29.8% saved)

bsearch88.0ms (0.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
44.0ms	-1.3457237152912733e-136	-2.2827810051209311e-144
9.0ms	-5.642449152827116e-86	-5.1255777530406294e-86
35.0ms	-4.8678311562813576e-74	-6.662044007232661e-77

Results

32.0ms	71×	body	1024	valid
31.0ms	186×	body	256	valid
21.0ms	47×	body	512	valid

Compiler

Compiled 408 to 324 computations (20.6% saved)

regimes53.0ms (0.3%)

Counts

3 → 4

Calls

Call 1

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

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

Calls

5 calls:

15.0ms	th
13.0ms	a1
10.0ms	a2
7.0ms	(*.f64 a1 a1)
7.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
27.8b	4	`a1`
28.2b	2	`a2`
36.0b	4	`th`
30.3b	2	`(*.f64 a1 a1)`
31.1b	2	`(*.f64 a2 a2)`

Compiler

Compiled 45 to 32 computations (28.9% saved)

bsearch91.0ms (0.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
44.0ms	-1.3457237152912733e-136	-2.2827810051209311e-144
10.0ms	-5.642449152827116e-86	-5.1255777530406294e-86
37.0ms	-4.8678311562813576e-74	-6.662044007232661e-77

Results

37.0ms	183×	body	256	valid
32.0ms	72×	body	1024	valid
16.0ms	49×	body	512	valid

Compiler

Compiled 408 to 324 computations (20.6% saved)

regimes51.0ms (0.3%)

Accuracy

Total -27.0b remaining (-97.1%)

Threshold costs -27.0b (-97.1%)

Counts

2 → 4

Calls

Call 1

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

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

Calls

5 calls:

13.0ms	(*.f64 a2 a2)
11.0ms	th
11.0ms	a1
8.0ms	a2
6.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.8b	4	`a1`
28.2b	2	`a2`
36.0b	4	`th`
30.3b	2	`(*.f64 a1 a1)`
31.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 39 to 28 computations (28.2% saved)

bsearch78.0ms (0.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
39.0ms	-1.3457237152912733e-136	-2.2827810051209311e-144
7.0ms	-5.642449152827116e-86	-5.1255777530406294e-86
31.0ms	-4.8678311562813576e-74	-6.662044007232661e-77

Results

32.0ms	201×	body	256	valid
28.0ms	63×	body	1024	valid
14.0ms	40×	body	512	valid

Compiler

Compiled 408 to 324 computations (20.6% saved)

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`*-commutative`
18×	`if-if-or-not`
8×	`not-or`
4×	`+-commutative`
4×	`not-not`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	1505
1	203	1475
2	209	1475
3	215	1467
4	217	1467
5	219	1467

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 5237424972633827/209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844544589904418936665155413025765720064) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 2912192802639553/4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a2 450559765389567/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (.f64 a2 a2))))))
(if (<=.f64 a2 1361730492884795/209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844544589904418936665155413025765720064) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 2348542582773833/4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a2 4405473261586877/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (/.f64 a2 (sqrt.f64 2)) (*.f64 (cos.f64 th) a2)))))
(if (<=.f64 a2 6837982044270725/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 70456277483215/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 a2 450559765389567/33374797436264220037422214158899251790667258161822699530422525122222183215322508594108782608384) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 (cos.f64 th) a2)))))
(if (<=.f64 a2 576116746989721/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 8830520111229613/18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078149624255479808) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 a2 4325373747739843/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a2 6033513568474169/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 70456277483215/146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 a2 2603234200028609/133499189745056880149688856635597007162669032647290798121690100488888732861290034376435130433536) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a2 7122897962782005/418993997810706159361688281193932691483730181893512293053861295116305125939798343025058571817715732115313495568327689089179808837873330310826051531440128) (.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (if (<=.f64 a2 8830520111229613/18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078149624255479808) (.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2)) (if (<=.f64 a2 5339967589802275/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a2 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2)))))
(if (<=.f64 a2 5656418970444533/209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844544589904418936665155413025765720064) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (if (<=.f64 a2 5166793682102433/9394170331095332911557922387157348109502730195633279482829163886128836100458433773854795993539074812127739904) (.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2)) (if (<=.f64 a2 7075457056488015/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2)))))
(if (<=.f64 th -57000000000000) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (if (<=.f64 th 86000000) (.f64 (pow.f64 1/4 1/4) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 -1/2 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))))) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a1 -496527519231531/63657374260452690195888927762793067532858387302060507832379389042324415617604272068231168) (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (if (<=.f64 a1 -3849561275618101/69992023193056381579920071267763883691301421788582797965624659405118495974380029543152421664737722368) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (if (<=.f64 a1 -1728350240969163/52374249726338269920211035149241586435466272736689036631732661889538140742474792878132321477214466514414186946040961136147476104734166288853256441430016) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(if (<=.f64 a1 -1941549914943807/63657374260452690195888927762793067532858387302060507832379389042324415617604272068231168) (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (if (<=.f64 a1 -7839106597622315/139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (if (<=.f64 a1 -1361730492884795/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(if (<=.f64 a1 -6029626489950079/32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016) (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (if (<=.f64 a1 -927394307307997/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (if (<=.f64 a1 -1501674488153571/858099707516326214372737599885174152158679412517913176174307932398192897924707006515319955082681819372162038923935107254640248499964580476571753536389382144) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))
(if (<=.f64 a1 -5983793180482553/127314748520905380391777855525586135065716774604121015664758778084648831235208544136462336) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a1 -927394307307997/17498005798264095394980017816940970922825355447145699491406164851279623993595007385788105416184430592) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (if (<=.f64 a1 -2513963986864237/1675975991242824637446753124775730765934920727574049172215445180465220503759193372100234287270862928461253982273310756356719235351493321243304206125760512) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))

Outputs
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(if (<=.f64 a2 5237424972633827/209496998905353079680844140596966345741865090946756146526930647558152562969899171512529285908857866057656747784163844544589904418936665155413025765720064) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 a2 2912192802639553/4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952) (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a2 450559765389567/16687398718132110018711107079449625895333629080911349765211262561111091607661254297054391304192) (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (.f64 (pow.f64 2 -1/2) (.f64 (cos.f64 th) (.f64 a2 a2))))))
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(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
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(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a1 a1) (sqrt.f64 1/2))

Compiler

Compiled 570 to 386 computations (32.3% saved)

soundness90.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

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
0	435	9563
1	1120	9125
2	5292	8945

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 128 to 69 computations (46.1% saved)

end200.0ms (1.2%)

Remove: (sort a1 a2)
Compiler: Compiled 554 to 320 computations (42.2% 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