Details

analyze410.0ms (2.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
25%	25%	74.9%	0.1%	0%	0%	0%	6
25%	25%	74.9%	0.1%	0%	0%	0%	7
25%	25%	74.9%	0.1%	0%	0%	0%	8
25%	25%	74.9%	0.1%	0%	0%	0%	9
28.1%	25%	64%	0.1%	10.9%	0%	0%	10
36.4%	31.2%	54.6%	0.1%	14%	0%	0%	11
46.9%	39%	44.1%	0.1%	16.8%	0%	0%	12

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.2s (26%)

Results

1.2s	1578×	body	1024	infinite
1.2s	1927×	body	1024	valid
1.0s	5397×	body	256	valid
296.0ms	928×	body	512	valid
269.0ms	771×	body	512	infinite
248.0ms	1549×	body	256	infinite
8.0ms	4×	body	2048	valid

Bogosity

preprocess29.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2

Call 2

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

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

Symmetry

(sort a1 a2)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 4

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (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

0.7b

Counts

5 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Status

Error

Program

▶

0.8b

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

▶

0.8b

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

▶

0.7b

(*.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 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.4b	(.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)

series12.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite95.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	280	69
2	3399	69

Stop Event

1×	node limit

Counts

3 → 206

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)))
(fma.f64 a1 a1 (*.f64 a2 a2))

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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((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 (.f64 a1 a1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a1 a1) 1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1 (.f64 (.f64 a1 a1) 1)) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 (.f64 a1 a1) 1) 1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 a2 a2))) (-.f64 1 (.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 a1 a1) (exp.f64 (log1p.f64 (.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (.f64 (.f64 a1 a1) 1) (exp.f64 (log1p.f64 (.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 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Outputs

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

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

simplify153.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac`
950×	`distribute-lft-neg-in`
922×	`associate-r`
822×	`associate-l`
622×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	517	11182
1	1295	10634
2	6582	10454

Stop Event

1×	node limit

Counts

290 → 312

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

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

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.6b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series4.0ms (0%)

Counts

3 → 64

Calls

18 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))

rewrite104.0ms (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	65
1	299	61
2	4071	61

Stop Event

1×	node limit

Counts

3 → 265

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

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

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1204×	`associate-/r*`
1106×	`associate-r`
1030×	`associate-/l/`
878×	`associate-l`
738×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	719	17331
1	2004	17125

Stop Event

1×	node limit

Counts

329 → 440

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

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 (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)))))
(+.f64 (+.f64 (.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (*.f64 th th)))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))) (+.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 (/.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 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (/.f64 (.f64 1/24 (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(fma.f64 -1/720 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (/.f64 (.f64 1/24 (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
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(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (/.f64 (+.f64 (pow.f64 a2 4) (-.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 (hypot.f64 a1 a2) 2))
(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(.f64 (/.f64 (sqrt.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)))) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))))
(.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (cbrt.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))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (/.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (/.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))))
(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (.f64 (pow.f64 a1 6) (pow.f64 a1 6)) (.f64 (pow.f64 a2 6) (pow.f64 a2 6))) (.f64 (+.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))))
(/.f64 (-.f64 (pow.f64 a1 12) (pow.f64 a2 12)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (-.f64 (pow.f64 a1 12) (pow.f64 a2 12)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (-.f64 (.f64 (pow.f64 a1 4) (pow.f64 a1 4)) (.f64 (pow.f64 a2 4) (pow.f64 a2 4))) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(/.f64 (-.f64 (pow.f64 a1 8) (pow.f64 a2 8)) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a1 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (+.f64 (.f64 (pow.f64 a1 6) (pow.f64 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 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 12) (-.f64 (pow.f64 a2 12) (*.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a1 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (+.f64 (pow.f64 a1 12) (pow.f64 a2 12)) (*.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 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 (pow.f64 (pow.f64 a1 4) 3) (pow.f64 (pow.f64 a2 4) 3)) (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (pow.f64 a1 8) (+.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) (pow.f64 a2 4))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (neg.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(neg.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (neg.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (+.f64 a2 a1) (neg.f64 (-.f64 a1 a2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(-.f64 (/.f64 (pow.f64 a1 4) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (pow.f64 a2 4) (*.f64 (-.f64 a1 a2) (+.f64 a2 a1))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (/.f64 (-.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 (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 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (+.f64 a1 a2)) (-.f64 a1 a2))
(-.f64 (/.f64 (pow.f64 a1 4) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (pow.f64 a2 4) (*.f64 (-.f64 a1 a2) (+.f64 a2 a1))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.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 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (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 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2))))))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.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)))))))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))))
(pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 3)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)
(pow.f64 (hypot.f64 a1 a2) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(pow.f64 (hypot.f64 a1 a2) 2)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3))
(pow.f64 (hypot.f64 a1 a2) 2)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 a1 a2))))
(pow.f64 (exp.f64 2) (log.f64 (hypot.f64 a1 a2)))
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a1 a2))) 1))
(pow.f64 (exp.f64 2) (log.f64 (hypot.f64 a1 a2)))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 (.f64 a2 a2)) (.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (.f64 a1 a1)) (.f64 a2 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 a2 a2))
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.6b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series8.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite120.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1474×	`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 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 (/.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 a1 a1) (*.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (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 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 (*.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 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 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 (*.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 (*.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 (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 (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 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)) a2 (*.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))))))))

simplify235.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1740×	`associate-/l*`
1664×	`associate-/l/`
1020×	`associate-r`
1006×	`associate-/r/`
884×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	822	21825
1	2394	21803

Stop Event

1×	node limit

Counts

383 → 538

Calls

Call 1

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

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

eval906.0ms (5.5%)

Compiler: Compiled 36939 to 21264 computations (42.4% saved)

prune488.0ms (3%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	1384	24	1408
Fresh	0	0	0
Picked	1	0	1
Done	2	0	2
Total	1387	24	1411

Error

Counts

1411 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.8b	(/.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2)) (/.f64 1 (cos.f64 th)))
	0.7b	(/.f64 (/.f64 (.f64 (cos.f64 th) (fma.f64 a1 a1 (.f64 a2 a2))) (pow.f64 2 1/4)) (pow.f64 2 1/4))
▶	0.5b	(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
	36.0b	(/.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
	36.1b	(/.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)))
	28.5b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
▶	28.4b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	28.1b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
▶	1.0b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))
	1.1b	(/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2))))
	27.5b	(+.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	27.5b	(+.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
	28.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	28.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
▶	27.6b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	0.7b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
▶	1.1b	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	0.7b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
	28.4b	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	28.5b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	0.7b	(.f64 (cos.f64 th) (+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1))))
	0.7b	(.f64 (cos.f64 th) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 2 -1/2)))
	0.6b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 798 to 562 computations (29.6% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 a1 a2))
✓	0.3b	(/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2)))
✓	0.3b	(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
✓	0.5b	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))

Compiler

Compiled 49 to 24 computations (51% saved)

series26.0ms (0.2%)

Counts

4 → 120

Calls

30 calls:

Time	Variable		Point	Expression
4.0ms	a2	@	0	(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
3.0ms	a1	@	0	(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
3.0ms	a1	@	-inf	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))
2.0ms	a2	@	0	(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))
2.0ms	a1	@	inf	(/.f64 1 (hypot.f64 a1 a2))

rewrite114.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1722×	`associate-/r/`
1382×	`associate-/l/`
316×	`add-sqr-sqrt`
308×	`*-un-lft-identity`
306×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	98
1	316	80
2	4245	80

Stop Event

1×	node limit

Counts

4 → 220

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2)))
(/.f64 1 (hypot.f64 a1 a2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) (/.f64 1 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (hypot.f64 a1 a2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (sqrt.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) -1/2) (/.f64 (sqrt.f64 2) (sqrt.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (cbrt.f64 (.f64 2 (pow.f64 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simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1788×	`associate-/l*`
1734×	`associate-r`
1546×	`associate-l`
1174×	`associate-/r*`
812×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	914	16720
1	2763	16396

Stop Event

1×	node limit

Counts

340 → 502

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) a2)
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (/.f64 (sqrt.f64 2) a2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (+.f64 (.f64 -1 (.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a2 5))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a2 5)))))) (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (+.f64 (.f64 -1 (.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a2 5))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a2 5)))))) (+.f64 (.f64 -1 (.f64 (pow.f64 a1 6) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a2 5))) (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a2 5)))) (pow.f64 a2 2))) (.f64 1/8 (/.f64 (sqrt.f64 2) (pow.f64 a2 7)))))) (/.f64 (sqrt.f64 2) a2))))
(/.f64 (sqrt.f64 2) a1)
(+.f64 (/.f64 (sqrt.f64 2) a1) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))))
(+.f64 (/.f64 (sqrt.f64 2) a1) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (.f64 -1 (/.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (.f64 -1/8 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 5)))))
(+.f64 (/.f64 (sqrt.f64 2) a1) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 5))) (.f64 -1 (/.f64 (+.f64 (.f64 -1/2 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 a2 6)))) (pow.f64 a1 7))))))
(*.f64 -1 (/.f64 (sqrt.f64 2) a1))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a1)) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a1)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 5))) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 5))))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 7))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2)) (pow.f64 a1 7))) (+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a1)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 5))) (.f64 -1/4 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 5))))))))
(/.f64 (sqrt.f64 2) a1)
(+.f64 (/.f64 (sqrt.f64 2) a1) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))))
(+.f64 (/.f64 (sqrt.f64 2) a1) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a1 5))) (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a1 5)))) (pow.f64 a2 4)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/8 (/.f64 (sqrt.f64 2) (pow.f64 a1 7))) (.f64 -1/2 (/.f64 (+.f64 (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a1 5))) (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a1 5)))) (pow.f64 a1 2)))) (pow.f64 a2 6))) (+.f64 (/.f64 (sqrt.f64 2) a1) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 3))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (/.f64 (sqrt.f64 2) (pow.f64 a1 5))) (.f64 -1/8 (/.f64 (sqrt.f64 2) (pow.f64 a1 5)))) (pow.f64 a2 4))))))
(/.f64 (sqrt.f64 2) a2)
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (/.f64 (sqrt.f64 2) a2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a1 4))) (.f64 -1/4 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 5))) (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a1 4))) (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))))) (.f64 1/8 (.f64 (sqrt.f64 2) (pow.f64 a1 6)))) (pow.f64 a2 7))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a1 4))) (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 5))) (/.f64 (sqrt.f64 2) a2))))
(*.f64 -1 (/.f64 (sqrt.f64 2) a2))
(+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a2)) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))))
(+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 5))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 5))) (+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a2)) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 2) (pow.f64 a1 4))) (.f64 -1/4 (.f64 (sqrt.f64 2) (pow.f64 a1 4))))) (pow.f64 a2 7))) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 7))) (+.f64 (.f64 -1/4 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 5))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 5))) (+.f64 (.f64 -1 (/.f64 (sqrt.f64 2) a2)) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 3))))))))
(/.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 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (cos.f64 th))) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 12) (.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4)))))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))) (.f64 1/256 (/.f64 1 (pow.f64 a2 10)))))) (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (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 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.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 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.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)))
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(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
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(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
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(sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 2))) (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 4))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 2))) (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 4))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 2))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (pow.f64 th 6))) (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (cos.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (cos.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (cos.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (cos.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (cos.f64 th))
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(.f64 (/.f64 1 (cbrt.f64 (.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (cbrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) -1) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (neg.f64 (hypot.f64 a1 a2))))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (neg.f64 (sqrt.f64 2)) (hypot.f64 a1 a2))) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (.f64 -1 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (*.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (sqrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (sqrt.f64 2)) (.f64 (sqrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (hypot.f64 a1 a2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) 1) (.f64 (/.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (sqrt.f64 2)) (hypot.f64 a1 a2)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (hypot.f64 a1 a2)) (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (hypot.f64 a1 a2)))
(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (hypot.f64 a1 a2)) (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) 1) (hypot.f64 a1 a2)))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(.f64 (.f64 (cos.f64 th) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))) (*.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (*.f64 (hypot.f64 a1 a2) (cbrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (sqrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (cbrt.f64 (.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (.f64 (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) (cbrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) (/.f64 1 (hypot.f64 a1 a2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))) (/.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) (cbrt.f64 (.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (.f64 (sqrt.f64 2) -1)) (*.f64 (hypot.f64 a1 a2) (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (cos.f64 th) (.f64 (neg.f64 (sqrt.f64 2)) 1)) (*.f64 (neg.f64 (hypot.f64 a1 a2)) (hypot.f64 a1 a2)))
(.f64 (/.f64 (cos.f64 th) (.f64 (neg.f64 (sqrt.f64 2)) -1)) (*.f64 (neg.f64 (hypot.f64 a1 a2)) (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2))) (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) -1) (neg.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (*.f64 (sqrt.f64 2) -1)) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) 1)) (hypot.f64 a1 a2))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (sqrt.f64 (hypot.f64 a1 a2)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) 1) (hypot.f64 a1 a2))
(.f64 (/.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) 1) (neg.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) -1/2)) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) -1) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2))) (cos.f64 th))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -1/2)) (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) (.f64 (cos.f64 th) (cbrt.f64 (hypot.f64 a1 a2))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 -1 (hypot.f64 a1 a2))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) -1) (.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 (/.f64 1 (hypot.f64 a1 a2)) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (/.f64 1 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (hypot.f64 a1 a2)))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))) -1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 2)))) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) 1) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) -1) (hypot.f64 a1 a2))
(.f64 (/.f64 (.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))) 1) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))) (pow.f64 2 1/4)) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) (sqrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) 1) (cbrt.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(pow.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)
(pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)) -1)
(neg.f64 (*.f64 (/.f64 (cos.f64 th) (/.f64 (neg.f64 (sqrt.f64 2)) (hypot.f64 a1 a2))) (hypot.f64 a1 a2)))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) 3) (pow.f64 (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)))) 1)
(*.f64 (hypot.f64 a1 a2) (cos.f64 th))
(*.f64 (cos.f64 th) (hypot.f64 a1 a2))
(*.f64 (cos.f64 th) (neg.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 1 (.f64 (hypot.f64 a1 a2) (cos.f64 th)))
(.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th)) 1)
(.f64 (sqrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a1 a2)))
(.f64 (sqrt.f64 (hypot.f64 a1 a2)) (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))))
(.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) (pow.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2) (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (cbrt.f64 (cos.f64 th)) (hypot.f64 a1 a2)))
(*.f64 (neg.f64 (hypot.f64 a1 a2)) (neg.f64 (cos.f64 th)))
(*.f64 (neg.f64 (cos.f64 th)) (neg.f64 (hypot.f64 a1 a2)))
(.f64 -1 (.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))))
(.f64 (.f64 (cos.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) (.f64 (cos.f64 th) (cbrt.f64 (hypot.f64 a1 a2))))
(*.f64 (/.f64 (cos.f64 th) -1) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (hypot.f64 a1 a2)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (hypot.f64 a1 a2)) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (cbrt.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) 1) (hypot.f64 a1 a2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 (hypot.f64 a1 a2) -1/2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -1/2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) (cbrt.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 1 (/.f64 (/.f64 1 (hypot.f64 a1 a2)) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 1 (/.f64 1 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (hypot.f64 a1 a2)))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 1 (hypot.f64 a1 a2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))) 1) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (cos.f64 th) (sqrt.f64 (hypot.f64 a1 a2))) (sqrt.f64 -1)) (sqrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) 1) (cbrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))) -1) (cbrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(pow.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) 1)
(pow.f64 (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) 3) 1/3)
(pow.f64 (/.f64 1 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))) -1)
(neg.f64 (*.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))))
(sqrt.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) 2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (hypot.f64 a1 a2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th)) 3))
(cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 3))))
(expm1.f64 (log1p.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(exp.f64 (.f64 (log.f64 (.f64 (hypot.f64 a1 a2) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (cos.f64 th))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (hypot.f64 a1 a2)))) 1)
(*.f64 1 (/.f64 1 (hypot.f64 a1 a2)))
(*.f64 (/.f64 1 (hypot.f64 a1 a2)) 1)
(*.f64 (pow.f64 (hypot.f64 a1 a2) -1/2) (pow.f64 (hypot.f64 a1 a2) -1/2))
(*.f64 (/.f64 1 (cbrt.f64 (hypot.f64 a1 a2))) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2)))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2)) (/.f64 1 (cbrt.f64 (hypot.f64 a1 a2))))
(*.f64 (/.f64 -1 (hypot.f64 a1 a2)) -1)
(*.f64 -1 (/.f64 -1 (hypot.f64 a1 a2)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)) (/.f64 1 (cbrt.f64 (hypot.f64 a1 a2))))
(*.f64 (pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) -1) (pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) -1) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) -1))
(*.f64 (/.f64 1 (/.f64 1 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) -2)))) (/.f64 1 (cbrt.f64 (hypot.f64 a1 a2))))
(pow.f64 (hypot.f64 a1 a2) -1)
(pow.f64 (/.f64 1 (hypot.f64 a1 a2)) 1)
(pow.f64 (pow.f64 (hypot.f64 a1 a2) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (hypot.f64 a1 a2))) 3)
(pow.f64 (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 3)) 1/3)
(pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1/2)
(sqrt.f64 (pow.f64 (hypot.f64 a1 a2) -2))
(log.f64 (exp.f64 (/.f64 1 (hypot.f64 a1 a2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (hypot.f64 a1 a2)))))
(cbrt.f64 (/.f64 1 (pow.f64 (hypot.f64 a1 a2) 3)))
(expm1.f64 (log1p.f64 (/.f64 1 (hypot.f64 a1 a2))))
(exp.f64 (neg.f64 (log.f64 (hypot.f64 a1 a2))))
(exp.f64 (*.f64 (log.f64 (hypot.f64 a1 a2)) -1))
(exp.f64 (*.f64 (neg.f64 (log.f64 (hypot.f64 a1 a2))) 1))
(log1p.f64 (expm1.f64 (/.f64 1 (hypot.f64 a1 a2))))

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

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 38 to 19 computations (50% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite91.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1542×	`associate-*r/`
1280×	`associate-*l/`
598×	`distribute-lft-in`
556×	`associate-/r*`
412×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	273	28
2	3532	28

Stop Event

1×	node limit

Counts

2 → 208

Calls

Call 1

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

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

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1536×	`associate-/l*`
950×	`times-frac`
760×	`associate-/r*`
686×	`associate-l`
670×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	10846
1	1430	10500
2	7946	10500

Stop Event

1×	node limit

Counts

232 → 297

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cos.f64 th) (.f64 a1 a1))
✓	0.4b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series1.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite70.0ms (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 a1 a1)) (sqrt.f64 2))
(.f64 (cos.f64 th) (.f64 a1 a1))

Outputs

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

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

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1274×	`unswap-sqr`
1092×	`*-commutative`
984×	`associate-/r*`
786×	`times-frac`
644×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4318
1	658	4250
2	2460	4210

Stop Event

1×	node limit

Counts

134 → 142

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.6b	(/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2)))
✓	0.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (*.f64 a2 a2))))

Compiler

Compiled 41 to 16 computations (61% saved)

series3.0ms (0%)

Counts

2 → 60

Calls

15 calls:

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

rewrite78.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1620×	`associate-*r/`
1456×	`associate-/l*`
1292×	`associate-*l/`
498×	`associate-/r/`
292×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	286	56
2	3652	56

Stop Event

1×	node limit

Counts

2 → 122

Calls

Call 1

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

Outputs

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

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

918×	`distribute-lft-in`
910×	`distribute-rgt-in`
644×	`distribute-lft-neg-in`
556×	`distribute-rgt-neg-in`
552×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	8366
1	1104	7824
2	4620	7776

Stop Event

1×	node limit

Counts

182 → 215

Calls

Call 1

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

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

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
✓	0.6b	(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
✓	0.6b	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
✓	1.0b	(/.f64 1 (pow.f64 2 1/4))

Compiler

Compiled 70 to 43 computations (38.6% saved)

series37.0ms (0.2%)

Counts

4 → 60

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	th	@	inf	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
5.0ms	a1	@	inf	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
1.0ms	th	@	0	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
0.0ms	th	@	0	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite121.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1742×	`associate-/r*`
1454×	`associate-/l*`
386×	`add-sqr-sqrt`
370×	`*-un-lft-identity`
368×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	102
1	391	72
2	5204	72

Stop Event

1×	node limit

Counts

4 → 367

Calls

Call 1

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

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

simplify254.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1566×	`associate-/l/`
1424×	`associate-/r*`
1208×	`associate-r`
1078×	`associate-l`
934×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	904	19961
1	2293	19345

Stop Event

1×	node limit

Counts

427 → 579

Calls

Call 1

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

eval996.0ms (6.1%)

Compiler: Compiled 45820 to 27438 computations (40.1% saved)

prune683.0ms (4.2%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	1878	22	1900
Fresh	15	4	19
Picked	1	0	1
Done	4	0	4
Total	1898	26	1924

Error

Counts

1924 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	27.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
	44.5b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a1 a1)) (sqrt.f64 2))
	28.5b	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
	42.7b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.1b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	40.4b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	28.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	28.5b	(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
	42.7b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.4b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	27.5b	(+.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
	0.7b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	28.1b	(*.f64 (/.f64 (cos.f64 th) (/.f64 1 a1)) (/.f64 a1 (sqrt.f64 2)))
	27.6b	(.f64 (/.f64 1 (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	42.7b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	40.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	27.5b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
▶	28.3b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
	0.7b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
	28.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	28.3b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
▶	40.4b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
▶	28.0b	(.f64 a1 (.f64 (pow.f64 2 -1/2) (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 658 to 490 computations (25.5% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	0.4b	(.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Compiler

Compiled 47 to 14 computations (70.2% saved)

series10.0ms (0.1%)

Counts

3 → 96

Calls

24 calls:

Time	Variable		Point	Expression
7.0ms	a1	@	inf	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	th	@	-inf	(.f64 (sqrt.f64 1/2) (.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 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	a2	@	0	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite116.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	75
1	293	69
2	3803	69

Stop Event

1×	node limit

Counts

3 → 236

Calls

Call 1

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

Outputs

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

simplify218.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1272×	`associate-/l*`
1050×	`associate-r`
940×	`associate-l`
730×	`+-commutative`
568×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	607	15534
1	1633	15132
2	7352	15132

Stop Event

1×	node limit

Counts

332 → 346

Calls

Call 1

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

Outputs
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 -1/2 (fma.f64 a2 a2 (.f64 a1 a1))) (*.f64 th th)))
(fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (.f64 th th) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) -1/2))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 -1/2 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.f64 1/24 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 th 4)))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4)) (.f64 (.f64 th th) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) -1/2)))))
(+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/2 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4))) (.f64 -1/720 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (fma.f64 -1/2 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4)) (.f64 -1/720 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 th 6))))))
(fma.f64 a2 a2 (fma.f64 a1 a1 (fma.f64 -1/2 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4)) (.f64 (pow.f64 th 6) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) -1/720))))))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (pow.f64 a1 2) (cos.f64 th))
(.f64 (cos.f64 th) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(*.f64 (cos.f64 th) (pow.f64 a2 2))
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (.f64 (pow.f64 a1 2) (cos.f64 th)))
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(.f64 (/.f64 (hypot.f64 (pow.f64 a2 3) (pow.f64 a1 3)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)))) (hypot.f64 a2 a1))
(/.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (.f64 (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 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (/.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2))) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)))
(.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)))) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (pow.f64 a1 4) (pow.f64 a1 4))) (/.f64 1 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(/.f64 (-.f64 (pow.f64 a2 8) (pow.f64 a1 8)) (.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(/.f64 (.f64 (-.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (pow.f64 a1 4) 3)) (/.f64 1 (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (+.f64 (.f64 (pow.f64 a1 4) (pow.f64 a1 4)) (.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (pow.f64 a1 4) 3)) (.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (+.f64 (pow.f64 a2 8) (pow.f64 a1 8)) (.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(/.f64 (/.f64 (-.f64 (pow.f64 a2 12) (pow.f64 a1 12)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (+.f64 (pow.f64 a2 8) (fma.f64 (pow.f64 a2 4) (pow.f64 a1 4) (pow.f64 a1 8))))
(/.f64 (.f64 (-.f64 (.f64 (pow.f64 a2 6) (pow.f64 a2 6)) (.f64 (pow.f64 a1 6) (pow.f64 a1 6))) (/.f64 1 (+.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 (pow.f64 a2 12) (pow.f64 a1 12)) (.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (/.f64 (-.f64 (pow.f64 a2 12) (pow.f64 a1 12)) (-.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 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (/.f64 1 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (+.f64 (.f64 (pow.f64 a2 6) (pow.f64 a2 6)) (-.f64 (.f64 (pow.f64 a1 6) (pow.f64 a1 6)) (*.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (+.f64 (pow.f64 a2 12) (pow.f64 a1 12)) (*.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(/.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (fma.f64 (pow.f64 a1 6) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (pow.f64 a2 12))) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))
(/.f64 (/.f64 (-.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 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (-.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 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (-.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 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (-.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 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (+.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 (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 (+.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 (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 (+.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 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))
(pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 3)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) 1/3)
(pow.f64 (hypot.f64 a2 a1) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2))
(sqrt.f64 (pow.f64 (hypot.f64 a2 a1) 4))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2))))
(pow.f64 (hypot.f64 a2 a1) 2)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3))
(pow.f64 (hypot.f64 a2 a1) 2)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 a2 a1))))
(pow.f64 (hypot.f64 a2 a1) 2)
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a2 a1))) 1))
(pow.f64 (hypot.f64 a2 a1) 2)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (.f64 a1 a1)) (.f64 a2 a2))
(fma.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 (.f64 a2 a2)) (.f64 a1 a1))

localize69.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
✓	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	@	inf	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
0.0ms	a1	@	0	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

rewrite75.0ms (0.5%)

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

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)))))))))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

66 → 69

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 23 to 17 computations (26.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (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: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	198	17
2	2302	17

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1066×	`log-prod`
754×	`associate-+r+`
748×	`associate-+l+`
722×	`associate-r`
686×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	637
1	155	629
2	600	629
3	3134	629

Stop Event

1×	node limit

Counts

35 → 34

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 12 computations (57.1% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite86.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	218	27
2	2568	27

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1374×	`fma-def`
886×	`associate-+r+`
856×	`associate-+l+`
838×	`distribute-lft-in`
788×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1181
1	176	1181
2	700	1133
3	1959	1105
4	7056	1105

Stop Event

1×	node limit

Counts

37 → 35

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

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

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 a1 (cos.f64 th))
✓	0.2b	(.f64 a1 (.f64 (pow.f64 2 -1/2) (*.f64 a1 (cos.f64 th))))
✓	0.4b	(.f64 (pow.f64 2 -1/2) (.f64 a1 (cos.f64 th)))

Compiler

Compiled 34 to 19 computations (44.1% saved)

series4.0ms (0%)

Counts

3 → 52

Calls

18 calls:

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

rewrite120.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1092×	`*-commutative`
970×	`sqrt-prod`
942×	`unswap-sqr`
680×	`swap-sqr`
420×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	63
1	246	59
2	2910	59

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

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

Outputs

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

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

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

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1210×	`unswap-sqr`
1186×	`fma-def`
1012×	`*-commutative`
890×	`distribute-lft-in`
870×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2973
1	493	2901
2	1912	2787

Stop Event

1×	node limit

Counts

103 → 104

Calls

Call 1

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

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

eval316.0ms (1.9%)

Compiler: Compiled 13693 to 7891 computations (42.4% saved)

prune230.0ms (1.4%)

Pruning

36 alts after pruning (32 fresh and 4 done)

	Pruned	Kept	Total
New	634	15	649
Fresh	4	17	21
Picked	1	0	1
Done	0	4	4
Total	639	36	675

Error

Counts

675 → 36

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	27.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
	44.5b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a1 a1)) (sqrt.f64 2))
	28.5b	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
▶	42.7b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.1b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	40.4b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	28.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
▶	28.5b	(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
	42.7b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.4b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	42.7b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	40.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
▶	0.7b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	42.7b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
	27.6b	(.f64 (/.f64 1 (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	42.7b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	42.7b	(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
	27.5b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	44.5b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
✓	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
✓	28.3b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
	40.4b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	0.7b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
	28.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	42.6b	(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
	40.4b	(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
✓	40.4b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	44.6b	(.f64 a1 (.f64 (pow.f64 2 -1/2) (+.f64 a1 (.f64 -1/2 (.f64 a1 (*.f64 th th))))))
▶	40.4b	(.f64 a1 (.f64 (sqrt.f64 1/2) a1))
	40.4b	(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	28.0b	(.f64 a1 (.f64 a1 (*.f64 (cos.f64 th) (sqrt.f64 1/2))))
	54.6b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	54.6b	(*.f64 a1 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))))
	49.4b	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))

Compiler

Compiled 816 to 616 computations (24.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.1b	(/.f64 1 (cos.f64 th))
✓	0.3b	(/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th)))
✓	0.6b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 55 to 28 computations (49.1% saved)

series3.0ms (0%)

Counts

3 → 52

Calls

15 calls:

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

rewrite120.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1544×	`associate-/r*`
1048×	`associate-/l*`
648×	`associate-/r/`
372×	`add-sqr-sqrt`
356×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	367	59
2	4951	59

Stop Event

1×	node limit

Counts

3 → 235

Calls

Call 1

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

Outputs

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

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

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

simplify123.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1528×	`times-frac`
1200×	`associate-r`
1194×	`associate-/r*`
996×	`associate-l`
860×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	633	14381
1	1776	13799

Stop Event

1×	node limit

Counts

287 → 376

Calls

Call 1

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

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

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 a1 (.f64 (sqrt.f64 1/2) a1))
✓	0.4b	(*.f64 (sqrt.f64 1/2) a1)

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite55.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

1386×	`add-sqr-sqrt`
1370×	`*-un-lft-identity`
1268×	`add-cube-cbrt`
1248×	`add-cbrt-cube`
1234×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	156	28
2	1754	28

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

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

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1446×	`associate-r`
1292×	`associate-l`
1048×	`associate-+l+`
970×	`associate-+r+`
746×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	638
1	138	578
2	569	518
3	4233	518

Stop Event

1×	node limit

Counts

34 → 28

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) a1)) 1)
(pow.f64 (*.f64 (sqrt.f64 1/2) a1) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) a1)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) a1)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a1) 3) 1/3)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(log.f64 (pow.f64 (exp.f64 a1) (sqrt.f64 1/2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a1) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) a1)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) a1)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) a1)))
(-.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 (sqrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 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 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 2))
(log.f64 (pow.f64 (exp.f64 a1) (*.f64 (sqrt.f64 1/2) 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) a1)) 1)
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(pow.f64 (*.f64 (sqrt.f64 1/2) a1) 1)
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) a1)) 2)
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) a1)) 3)
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a1) 3) 1/3)
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(sqrt.f64 (.f64 a1 (.f64 a1 1/2)))
(log.f64 (pow.f64 (exp.f64 a1) (sqrt.f64 1/2)))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) a1) 3))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) a1)))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) a1)))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) a1)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) a1)))
(+.f64 (+.f64 1 (*.f64 (sqrt.f64 1/2) a1)) -1)
(+.f64 (*.f64 (sqrt.f64 1/2) a1) 0)
(*.f64 (sqrt.f64 1/2) 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 (sqrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 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 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(log.f64 (pow.f64 (exp.f64 a1) (*.f64 (sqrt.f64 1/2) 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))

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

Compiler

Compiled 16 to 10 computations (37.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

Outputs

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

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

46 → 45

Calls

Call 1

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

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

localize19.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
✓	11.8b	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a1 a1))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series4.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite88.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

886×	`swap-sqr`
766×	`associate-*r/`
680×	`distribute-rgt-in`
656×	`associate-*l/`
626×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	306	64
2	3661	64

Stop Event

1×	node limit

Counts

2 → 137

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 1 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 1 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th))) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1)) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th)))) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1))) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th))) 1) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1)) 1) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a1 a1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a1 a1))) (-.f64 1 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a1 a1))) (-.f64 1 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 a1 a1) (*.f64 -1/2 (*.f64 th th))) (exp.f64 (log1p.f64 (*.f64 a1 a1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a1 a1)) (exp.f64 (log1p.f64 (*.f64 a1 a1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 a1) (/.f64 1 (fma.f64 -1/2 (*.f64 th th) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (/.f64 (fma.f64 -1/2 (*.f64 th th) -1) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))) (/.f64 (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (+.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 a1 a1) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a1 a1)) (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 a1 a1)) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (*.f64 a1 a1) (+.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 a1 a1) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a1 a1))) (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 a1 a1))) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) a1)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (*.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))) a1)) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (+.f64 1 (*.f64 -1/4 (pow.f64 th 4)))) (+.f64 1 (*.f64 (*.f64 th th) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (+.f64 (neg.f64 (*.f64 1/4 (pow.f64 th 4))) 1)) (+.f64 1 (*.f64 (*.f64 th th) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a1 a1) (+.f64 -1 (neg.f64 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (neg.f64 (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a1 a1) (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 a1 a1) (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (sqrt.f64 (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a1 a1) (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 (*.f64 a1 a1) (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 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (*.f64 -1/4 (pow.f64 th 4))) (*.f64 a1 a1)) (+.f64 1 (*.f64 (*.f64 th th) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 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(fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))) (*.f64 a1 a1)) (+.f64 1 (+.f64 (*.f64 (*.f64 th th) 1/2) (*.f64 1/4 (pow.f64 th 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 1/2 1/4) (*.f64 a1 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/2 (*.f64 (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 2) (pow.f64 a1 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (pow.f64 (exp.f64 a1) a1) (fma.f64 -1/2 (*.f64 th th) 1)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a1 a1)) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a1 a1)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)))))))))

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1714×	`distribute-lft-in`
1584×	`associate-*r/`
1240×	`associate-/l/`
1102×	`associate-*l/`
1096×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	349	9355
1	921	8069
2	4125	8069

Stop Event

1×	node limit

Counts

185 → 207

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 31 to 19 computations (38.7% saved)

series5.0ms (0%)

Counts

3 → 52

Calls

15 calls:

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

rewrite145.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1250×	`associate-/r/`
880×	`associate-/l/`
876×	`unswap-sqr`
822×	`swap-sqr`
480×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	63
1	235	63
2	3214	63

Stop Event

1×	node limit

Counts

3 → 249

Calls

Call 1

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

Outputs

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

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

simplify139.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1078×	`associate-r`
1058×	`*-commutative`
954×	`associate-l`
782×	`associate-*r/`
706×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	636	9751
1	1857	9355
2	7789	9355

Stop Event

1×	node limit

Counts

301 → 348

Calls

Call 1

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

Outputs
(/.f64 (sqrt.f64 2) a2)
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) a2)) (/.f64 (sqrt.f64 2) a2))
(fma.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 a2 (*.f64 th th))) (/.f64 (sqrt.f64 2) a2))
(fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) a2) (.f64 th th)) (/.f64 (sqrt.f64 2) a2))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) a2)) (.f64 -1/4 (/.f64 (sqrt.f64 2) a2))) (pow.f64 th 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) a2)) (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1 (.f64 (.f64 (/.f64 (sqrt.f64 2) a2) -5/24) (pow.f64 th 4)) (fma.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 a2 (*.f64 th th))) (/.f64 (sqrt.f64 2) a2)))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) a2) (.f64 th th)) (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 (sqrt.f64 2) a2) (.f64 -5/24 (pow.f64 th 4))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) a2)) (.f64 -1/4 (/.f64 (sqrt.f64 2) a2))) (pow.f64 th 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) a2)) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (/.f64 (sqrt.f64 2) a2)) (.f64 -1/4 (/.f64 (sqrt.f64 2) a2)))) (+.f64 (.f64 -1/720 (/.f64 (sqrt.f64 2) a2)) (*.f64 1/48 (/.f64 (sqrt.f64 2) a2)))) (pow.f64 th 6))) (/.f64 (sqrt.f64 2) a2))))
(fma.f64 -1 (.f64 (.f64 (/.f64 (sqrt.f64 2) a2) -5/24) (pow.f64 th 4)) (fma.f64 1/2 (/.f64 (sqrt.f64 2) (/.f64 a2 (.f64 th th))) (fma.f64 -1 (.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) a2) -5/24) (.f64 (/.f64 (sqrt.f64 2) a2) 7/360)) (pow.f64 th 6)) (/.f64 (sqrt.f64 2) a2))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 (sqrt.f64 2) a2) (.f64 th th)) (fma.f64 (neg.f64 (fma.f64 (/.f64 (sqrt.f64 2) a2) 7/360 (.f64 (/.f64 (sqrt.f64 2) a2) -5/48))) (pow.f64 th 6) (/.f64 (sqrt.f64 2) a2))) (.f64 (/.f64 (sqrt.f64 2) a2) (*.f64 -5/24 (pow.f64 th 4))))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
(/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))
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(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (.f64 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 a2)))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (.f64 (.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 a2)) 1))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (.f64 1 (.f64 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))) (neg.f64 a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(neg.f64 (/.f64 (neg.f64 a2) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) a2))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))
(fabs.f64 (.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2))))
(log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(cbrt.f64 (/.f64 (pow.f64 a2 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) a2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 a2 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))) 3)))
(expm1.f64 (log1p.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(exp.f64 (log.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(.f64 a2 (.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a2 (/.f64 (.f64 a2 (cos.f64 th)) (sqrt.f64 2)))

eval539.0ms (3.3%)

Compiler: Compiled 23742 to 14739 computations (37.9% saved)

prune428.0ms (2.6%)

Pruning

37 alts after pruning (30 fresh and 7 done)

	Pruned	Kept	Total
New	1097	8	1105
Fresh	5	22	27
Picked	0	1	1
Done	2	6	8
Total	1104	37	1141

Error

Counts

1141 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	0.7b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	27.5b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
	44.5b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a1 a1)) (sqrt.f64 2))
✓	42.7b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.1b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	40.4b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	28.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
✓	28.5b	(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a2))
	28.5b	(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
	42.7b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.4b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	42.7b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	40.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	44.7b	(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 1)
	28.3b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (.f64 a1 a1))
	42.7b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
	27.6b	(.f64 (/.f64 1 (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
	42.7b	(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
	27.5b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	44.5b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
	56.4b	(.f64 (sqrt.f64 1/2) (.f64 (.f64 (.f64 (*.f64 -1/2 a1) a1) th) th))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
✓	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	28.3b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
	58.7b	(.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 (.f64 -1/2 th) (*.f64 th a1))))
	40.4b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	0.7b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
	28.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	42.6b	(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
	42.6b	(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))
✓	40.4b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
✓	40.4b	(.f64 a1 (.f64 (sqrt.f64 1/2) a1))
	40.4b	(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	28.0b	(.f64 a1 (.f64 a1 (*.f64 (cos.f64 th) (sqrt.f64 1/2))))
	58.9b	(.f64 a1 (.f64 a1 (.f64 -1/2 (.f64 th (*.f64 th (sqrt.f64 1/2))))))
	54.6b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	54.6b	(*.f64 a1 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))))

Compiler

Compiled 448 to 338 computations (24.6% saved)

regimes289.0ms (1.8%)

Counts

72 → 1

Calls

Call 1

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

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

Calls

8 calls:

63.0ms	(*.f64 a2 a2)
35.0ms	a2
33.0ms	a1
32.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
31.0ms	th

Results

Error	Segments	Branch
0.5b	1	`a1`
0.5b	1	`a2`
0.5b	1	`th`
0.5b	1	`(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))`
0.5b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.5b	1	`(cos.f64 th)`
0.5b	1	`(*.f64 a1 a1)`
0.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 845 to 450 computations (46.7% saved)

regimes213.0ms (1.3%)

Counts

69 → 1

Calls

Call 1

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

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

Calls

7 calls:

41.0ms	th
34.0ms	a1
32.0ms	a2
26.0ms	(cos.f64 th)
26.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.6b	1	`a1`
0.6b	1	`a2`
0.6b	1	`th`
0.6b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.6b	1	`(cos.f64 th)`
0.6b	1	`(*.f64 a1 a1)`
0.6b	1	`(*.f64 a2 a2)`

Compiler

Compiled 772 to 410 computations (46.9% saved)

regimes203.0ms (1.2%)

Counts

68 → 1

Calls

Call 1

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

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

Calls

7 calls:

32.0ms	(cos.f64 th)
30.0ms	a2
30.0ms	a1
30.0ms	th
28.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.7b	1	`a1`
0.7b	1	`a2`
0.7b	1	`th`
0.7b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.7b	1	`(cos.f64 th)`
0.7b	1	`(*.f64 a1 a1)`
0.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 758 to 403 computations (46.8% saved)

regimes185.0ms (1.1%)

Counts

64 → 1

Calls

Call 1

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

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

Calls

7 calls:

30.0ms	th
28.0ms	a1
27.0ms	a2
25.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
24.0ms	(cos.f64 th)

Results

Error	Segments	Branch
0.7b	1	`a1`
0.7b	1	`a2`
0.7b	1	`th`
0.7b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.7b	1	`(cos.f64 th)`
0.7b	1	`(*.f64 a1 a1)`
0.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 670 to 361 computations (46.1% saved)

regimes150.0ms (0.9%)

Counts

52 → 1

Calls

Call 1

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

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

Calls

7 calls:

26.0ms	a1
23.0ms	a2
23.0ms	th
19.0ms	(cos.f64 th)
19.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.7b	1	`a1`
0.7b	1	`a2`
0.7b	1	`th`
0.7b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.7b	1	`(cos.f64 th)`
0.7b	1	`(*.f64 a1 a1)`
0.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 511 to 294 computations (42.5% saved)

regimes824.0ms (5%)

Counts

51 → 4

Calls

Call 1

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

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

Calls

7 calls:

214.0ms	th
144.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
133.0ms	(cos.f64 th)
105.0ms	(*.f64 a1 a1)
100.0ms	a2

Results

Error	Segments	Branch
7.6b	2	`a1`
5.3b	4	`a2`
11.0b	6	`th`
11.0b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
11.0b	6	`(cos.f64 th)`
10.2b	4	`(*.f64 a1 a1)`
10.4b	4	`(*.f64 a2 a2)`

Compiler

Compiled 498 to 290 computations (41.8% saved)

bsearch117.0ms (0.7%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
17.0ms	2.436424451855572e-109	4.36881725282153e-109
36.0ms	3.781702939489577e-135	8.911527674473616e-134
63.0ms	3.344810061137985e-149	2.6731980277988346e-148

Results

48.0ms	23×	body	512	valid
37.0ms	83×	body	1024	valid
27.0ms	166×	body	256	valid

Compiler

Compiled 470 to 360 computations (23.4% saved)

regimes271.0ms (1.7%)

Counts

32 → 3

Calls

Call 1

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

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

Calls

6 calls:

93.0ms	th
57.0ms	a1
29.0ms	a2
25.0ms	(*.f64 a1 a1)
24.0ms	(cos.f64 th)

Results

Error	Segments	Branch
18.9b	2	`a1`
17.4b	2	`a2`
16.2b	3	`th`
16.3b	2	`(cos.f64 th)`
20.5b	2	`(*.f64 a1 a1)`
19.3b	2	`(*.f64 a2 a2)`

Compiler

Compiled 311 to 196 computations (37% saved)

bsearch48.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
27.0ms	1.0534917441824884e-8	0.07014499762374776
21.0ms	-40316773932.76103	-1367738435.044058

Results

44.0ms

256×

body

256

valid

Compiler

Compiled 460 to 340 computations (26.1% saved)

regimes76.0ms (0.5%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

5 calls:

17.0ms	a1
16.0ms	th
15.0ms	a2
10.0ms	(*.f64 a2 a2)
10.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.5b	1	`a1`
27.5b	1	`a2`
27.5b	1	`th`
27.5b	1	`(*.f64 a1 a1)`
27.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 288 to 182 computations (36.8% saved)

regimes115.0ms (0.7%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

5 calls:

50.0ms	th
17.0ms	a1
17.0ms	a2
16.0ms	(*.f64 a1 a1)
10.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
30.4b	2	`a1`
30.0b	2	`a2`
35.5b	6	`th`
32.3b	2	`(*.f64 a1 a1)`
32.9b	2	`(*.f64 a2 a2)`

Compiler

Compiled 153 to 101 computations (34% saved)

bsearch37.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
37.0ms	2.6731980277988346e-148	5.312118388821481e-147

Results

18.0ms	39×	body	1024	valid
14.0ms	63×	body	256	valid
4.0ms	10×	body	512	valid

Compiler

Compiled 168 to 132 computations (21.4% saved)

regimes11.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	th
3.0ms	a1
3.0ms	a2

Results

Error	Segments	Branch
40.4b	1	`a1`
40.4b	1	`a2`
40.4b	1	`th`

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	502
1	95	482
2	98	482
3	101	478
4	102	478
5	103	478

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
(.f64 (cos.f64 th) (+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
(if (<=.f64 a2 7486192554119879/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (if (<=.f64 a2 3109721077501335/818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (if (<=.f64 a2 7826902670476543/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))))
(if (<=.f64 th -1400000000) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (if (<=.f64 th 662929865148937/288230376151711744) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 a1 (.f64 a1 (*.f64 (cos.f64 th) (sqrt.f64 1/2))))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 8817871037304665/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (.f64 a1 (.f64 (sqrt.f64 1/2) a1)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(.f64 a1 (.f64 (sqrt.f64 1/2) a1))

Outputs
(/.f64 (/.f64 (cos.f64 th) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))
(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
(.f64 (cos.f64 th) (+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)))
(if (<=.f64 a2 7486192554119879/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (if (<=.f64 a2 3109721077501335/818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (if (<=.f64 a2 7826902670476543/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))))
(if (<=.f64 a2 7486192554119879/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (if (or (<=.f64 a2 3109721077501335/818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344) (not (<=.f64 a2 7826902670476543/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192))) (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2))) (.f64 a1 (.f64 a1 (*.f64 (cos.f64 th) (sqrt.f64 1/2))))))
(if (or (<=.f64 a2 7486192554119879/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208) (not (or (<=.f64 a2 3109721077501335/818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344) (not (<=.f64 a2 7826902670476543/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192))))) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2))))
(if (or (<=.f64 a2 7486192554119879/28793048285076456849987446449190283896766061557132266451844835664715760516297522370041860391064901485759493828054533728788532902755163518009654497157537048672862208) (and (not (<=.f64 a2 3109721077501335/818347651974035467503297424206899788054160511510766197370822842024033449101168638720817523081476039287721671031890017752304314136471348263332131897344)) (<=.f64 a2 7826902670476543/21153791001287955166461289857048673274508949854856999017108761448780985319561963066406054734070889115122918784800747465736192))) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2))))
(if (<=.f64 th -1400000000) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (if (<=.f64 th 662929865148937/288230376151711744) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 a1 (.f64 a1 (*.f64 (cos.f64 th) (sqrt.f64 1/2))))))
(if (or (<=.f64 th -1400000000) (not (<=.f64 th 662929865148937/288230376151711744))) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 8817871037304665/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (.f64 a1 (.f64 (sqrt.f64 1/2) a1)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a2 8817871037304665/3599131035634557106248430806148785487095757694641533306480604458089470064537190296255232548883112685719936728506816716098566612844395439751206812144692131084107776) (.f64 a1 (.f64 a1 (sqrt.f64 1/2))) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(.f64 a1 (.f64 (sqrt.f64 1/2) a1))
(.f64 a1 (.f64 a1 (sqrt.f64 1/2)))

Compiler

Compiled 194 to 137 computations (29.4% saved)

soundness19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 73 to 33 computations (54.8% saved)

end79.0ms (0.5%)

Remove: (sort a1 a2)
Compiler: Compiled 203 to 115 computations (43.3% 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