Details

analyze1.1s (14.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.3s (60.8%)

Results

1.2s	1766×	body	1024	valid
1.0s	1566×	body	1024	invalid
848.0ms	5053×	body	128	valid
430.0ms	985×	body	512	valid
395.0ms	844×	body	512	invalid
140.0ms	447×	body	256	valid
136.0ms	424×	body	256	invalid
120.0ms	690×	body	128	invalid
5.0ms	5×	body	2048	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 46 to 32 computations (30.4% saved)

preprocess28.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

96×	`fma-def_binary64`
70×	`*-commutative_binary64`
57×	`associate-/l*_binary64`
30×	`associate-/r/_binary64`
26×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	80
1	69	72
2	160	72
3	243	72
4	321	72
5	375	72
6	420	72
7	474	72
8	480	72
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 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)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (/.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)))

Symmetry

(sort a1 a2)

Compiler

Compiled 22 to 15 computations (31.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	58	18
3	88	18
4	115	18
5	135	18
6	152	18
7	170	18
8	172	18

Stop Event

1×

saturated

Counts

1 → 2

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)))

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.1b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series16.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

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

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
182×	`pow3_binary64`
171×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	224	36
2	2729	36

Stop Event

1×	node limit

Counts

3 → 94

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 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.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) (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 (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 (pow.f64 (cbrt.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 (/.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 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 (/.f64 (pow.f64 (cbrt.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 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(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 (pow.f64 (cbrt.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 (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 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 (pow.f64 (cbrt.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 pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(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 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(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 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -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 cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 2 (sqrt.f64 2))))))) (#(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 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 expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 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 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.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 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a1 a1) 1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(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 (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 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (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) (cbrt.f64 (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) ((x /.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (fma.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 (.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 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)))) (#(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 (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 log.f64 (.f64 (pow.f64 (exp.f64 a2) a2) (exp.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 a2 a2))) (exp.f64 (.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 a1 a1)) (+.f64 1 (expm1.f64 (.f64 a2 a2)))))))) (#(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 log1p.f64 (expm1.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 expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.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) (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 (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 (pow.f64 (cbrt.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 (/.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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 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 (/.f64 (pow.f64 (cbrt.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 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))))) (#(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 (pow.f64 (cbrt.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 (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 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 (pow.f64 (cbrt.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 pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)))) (#(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 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)))) (#(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 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -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 cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (*.f64 2 (sqrt.f64 2))))))) (#(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 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 expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))) 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 1 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cos.f64 th)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.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 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a1 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) 1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(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 (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 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (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) (cbrt.f64 (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) ((x /.f64 (+.f64 (pow.f64 (*.f64 a1 a1) 3) (pow.f64 (*.f64 a2 a2) 3)) (fma.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 (*.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 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)))) (#(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 (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 log.f64 (*.f64 (pow.f64 (exp.f64 a2) a2) (exp.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 a2 a2))) (exp.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 a1 a1)) (+.f64 1 (expm1.f64 (*.f64 a2 a2)))))))) (#(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 log1p.f64 (expm1.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 expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

488×	`associate-/r/_binary64`
338×	`unswap-sqr_binary64`
331×	`fma-neg_binary64`
276×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1517
1	201	1427
2	604	1383
3	2757	1341

Stop Event

1×	node limit

Counts

178 → 122

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

prune101.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	6	124

Error

Counts

124 → 6

Alt Table

Status	Error	Program
	0.5b	(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 2282 to 1457 computations (36.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a1 a2)
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))

series30.0ms (0.4%)

Counts

4 → 108

Calls

27 calls:

Time	Variable		Point	Expression
6.0ms	a2	@	inf	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
3.0ms	a1	@	0	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
3.0ms	a1	@	inf	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
3.0ms	a2	@	0	(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
2.0ms	th	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

rewrite52.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`log-prod_binary64`
208×	`pow1/3_binary64`
207×	`expm1-udef_binary64`
207×	`log1p-udef_binary64`
189×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	249	40
2	2782	40

Stop Event

1×	node limit

Counts

4 → 105

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))) 3)))) (#(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 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 (sqrt.f64 1/2) 1/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (.f64 (sqrt.f64 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (cos.f64 th)) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) (pow.f64 (cos.f64 th) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 4) 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(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 (hypot.f64 a1 a2) (hypot.f64 a1 a2))))) (#(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 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (.f64 (cbrt.f64 (hypot.f64 a1 a2)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a1 a2)) (.f64 (sqrt.f64 (hypot.f64 a1 a2)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) 3) (sqrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)) (cbrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 a1 a1) 3) (pow.f64 (.f64 a2 a2) 3)) (fma.f64 (.f64 a1 a1) (.f64 a1 a1) (-.f64 (.f64 (.f64 a2 a2) (.f64 a2 a2)) (.f64 (.f64 a1 a1) (.f64 a2 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a1 a2) 4))))) (#(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 log.f64 (.f64 (exp.f64 (.f64 a1 a1)) (exp.f64 (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 a2 a2)) (exp.f64 (.f64 a1 a1))))))) (#(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 log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 1))))) (#(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 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 (cbrt.f64 a2) 2)) (pow.f64 (cbrt.f64 a2) 2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 (cbrt.f64 a1) 2)) (pow.f64 (cbrt.f64 a1) 2) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a1 (sqrt.f64 a1)) (sqrt.f64 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a2 (sqrt.f64 a2)) (sqrt.f64 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a2 (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a1 (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 a1) (.f64 a2 a2))))) (#(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 +.f64 0 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (hypot.f64 a1 a2))) (cbrt.f64 (exp.f64 (hypot.f64 a1 a2))))) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a1 a2)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 a1 a2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a1 a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (cbrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 a1 a2)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a1 a2)) (sqrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 4))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a1 a2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a1 a2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 a1 a2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 a1 a2)))))))

simplify44.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
546×	`associate-r_binary64`
530×	`associate-l_binary64`
451×	`cancel-sign-sub-inv_binary64`
184×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	112	1905
1	365	1696
2	1259	1648

Stop Event

1×	node limit

Counts

213 → 163

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2))))))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 4)))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))
(-.f64 (+.f64 (.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 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 4) (pow.f64 a2 2))))))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 6)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(pow.f64 a2 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2) (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)) (*.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(-.f64 (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))) (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(*.f64 -1 a1)
(neg.f64 (+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(-.f64 (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))) (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2) (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)) (*.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(*.f64 -1 a2)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2))))))
(-.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 1/2 (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (.f64 th th))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 th th))))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 -1/2 (.f64 (.f64 th th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 th th) (fma.f64 a2 a2 (.f64 a1 a1)))) -1/2))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 4)))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))
(-.f64 (fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (fma.f64 1/24 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (pow.f64 th 4)) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (pow.f64 th 4))) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))) (.f64 1/2 (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (.f64 th th))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 th th))))))
(+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/24) (+.f64 (.f64 a2 (.f64 a2 (pow.f64 th 4))) (.f64 (.f64 a1 a1) (pow.f64 th 4)))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))) (.f64 -1/2 (.f64 (.f64 th th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 th th) (fma.f64 a2 a2 (.f64 a1 a1)))) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 4) (fma.f64 a2 a2 (.f64 a1 a1)))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1)))))
(-.f64 (+.f64 (.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 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 4) (pow.f64 a2 2))))))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 6)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))))
(-.f64 (fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (fma.f64 1/24 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (pow.f64 th 4)) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (pow.f64 th 4))) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))) (fma.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (pow.f64 th 6))) (fma.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (pow.f64 th 6))) (.f64 1/2 (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (.f64 a2 a2) (.f64 th th))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (.f64 th th))))))))
(-.f64 (-.f64 (+.f64 (.f64 (.f64 (sqrt.f64 1/2) 1/24) (+.f64 (.f64 a2 (.f64 a2 (pow.f64 th 4))) (.f64 (.f64 a1 a1) (pow.f64 th 4)))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))) (.f64 (.f64 (sqrt.f64 1/2) 1/720) (+.f64 (.f64 a2 (.f64 a2 (pow.f64 th 6))) (.f64 a1 (.f64 a1 (pow.f64 th 6)))))) (.f64 1/2 (.f64 (.f64 th th) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))))
(-.f64 (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 4) (fma.f64 a2 a2 (.f64 a1 a1)))) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))) (fma.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 th th) (fma.f64 a2 a2 (.f64 a1 a1)))) (.f64 (sqrt.f64 1/2) (.f64 1/720 (.f64 (pow.f64 th 6) (fma.f64 a2 a2 (*.f64 a1 a1)))))))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cos.f64 th))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2)
(fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)
(fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2) (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2) (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(+.f64 (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2) (*.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8))
(fma.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)) (*.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2)) (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)) (/.f64 (*.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(fma.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1))
(fma.f64 1/2 (/.f64 (*.f64 a2 a2) a1) a1)
(fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1)
(-.f64 (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))) (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 a1 (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) (.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8)))
(fma.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1))) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) a1)) (.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8))
(fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1)))
(*.f64 -1 a1)
(neg.f64 a1)
(neg.f64 (+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(neg.f64 (+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1)))
(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 a2 a2) a1) a1))
(fma.f64 (*.f64 (/.f64 a2 a1) a2) -1/2 (neg.f64 a1))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (+.f64 a1 (/.f64 (.f64 1/2 (*.f64 a2 a2)) a1)))
(fma.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) (neg.f64 (fma.f64 1/2 (/.f64 (*.f64 a2 a2) a1) a1)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (fma.f64 1/2 (.f64 (/.f64 a2 a1) a2) a1))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (+.f64 a1 (/.f64 (.f64 1/2 (*.f64 a2 a2)) a1))))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) a1)))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))) (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 1/2 (.f64 (/.f64 a2 a1) a2) a1)))
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1))
(fma.f64 1/2 (/.f64 (*.f64 a2 a2) a1) a1)
(fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1)
(-.f64 (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1))) (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1)) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 a1 (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) (.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8)))
(fma.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))) (*.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (+.f64 a1 (/.f64 (.f64 1/2 (.f64 a2 a2)) a1))) (*.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) a1)) (.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8))
(fma.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5)) (fma.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a2 a1) a2) a1)))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2)
(fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)
(fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2) (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2) (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(+.f64 (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2) (*.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8))
(fma.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8 (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)) (*.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2)) (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)) (/.f64 (*.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)))
(fma.f64 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) -1/8 (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)))
(*.f64 -1 a2)
(neg.f64 a2)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(neg.f64 (fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2))
(neg.f64 (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2))
(-.f64 (/.f64 -1/2 (/.f64 a2 (*.f64 a1 a1))) a2)
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2))
(-.f64 (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2))
(-.f64 (/.f64 (*.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)) (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (fma.f64 1/2 (.f64 (/.f64 a1 a2) a1) a2))
(-.f64 (.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5))) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)))
(-.f64 (/.f64 (.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)) (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) a2) a2)))
(-.f64 (/.f64 (*.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 3)) (fma.f64 1/16 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) (fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)))
(-.f64 (fma.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (.f64 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) -1/16)) (fma.f64 1/2 (.f64 (/.f64 a1 a2) a1) a2))

prune131.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	1	3	4
Picked	0	1	1
Done	1	0	1
Total	164	5	169

Error

Counts

169 → 5

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	0.5b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 3242 to 2038 computations (37.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.1b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.2b	(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
✓	0.4b	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

series9.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite46.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
194×	`pow3_binary64`
181×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	247	38
2	2850	38

Stop Event

1×	node limit

Counts

3 → 54

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2))) (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 3) (*.f64 (sqrt.f64 1/2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) 1/2) (pow.f64 (hypot.f64 a1 a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (hypot.f64 a1 a2) (sqrt.f64 1/2)) 3) (pow.f64 (hypot.f64 a1 a2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))) (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/4))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))))))

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
605×	`associate-l_binary64`
419×	`cancel-sign-sub-inv_binary64`
302×	`times-frac_binary64`
228×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1983
1	389	1812
2	1408	1780

Stop Event

1×	node limit

Counts

138 → 107

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))) (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))))
(.f64 -1 (.f64 (sqrt.f64 1/2) a1))
(neg.f64 (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))))
(-.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))))
(-.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))))
(*.f64 (sqrt.f64 1/2) a1)
(+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 6)) (pow.f64 a1 5))) (+.f64 (.f64 (sqrt.f64 1/2) a1) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) a1)))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a2 4)) (pow.f64 a1 3))))
(*.f64 (sqrt.f64 1/2) a2)
(+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))) (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))) (.f64 1/8 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))))
(.f64 -1 (.f64 (sqrt.f64 1/2) a2))
(neg.f64 (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2))))
(-.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2))))
(-.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 4)) (pow.f64 a2 3))) (+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 6)) (pow.f64 a2 5))) (+.f64 (.f64 (sqrt.f64 1/2) a2) (.f64 1/2 (/.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) a2)))))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(*.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2))))))
(-.f64 (+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 4)))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 4)))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))
(-.f64 (+.f64 (.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 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 4) (pow.f64 a2 2))))))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (pow.f64 th 6)))) (+.f64 (.f64 1/720 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 6)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (pow.f64 th 2)))) (.f64 1/2 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 th 2) (pow.f64 a2 2))))))))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (sqrt.f64 1/2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a1 2))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 a2 2))))

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

prune147.0ms (2.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
▶	0.5b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 4913 to 2931 computations (40.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 a1 2) (pow.f64 a2 2))
✓	0.2b	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓	0.3b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))

series8.0ms (0.1%)

Counts

3 → 46

Calls

18 calls:

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

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

598×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
134×	`add-sqr-sqrt_binary64`
131×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	275	32
2	3298	32

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

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

Outputs

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

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

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

simplify30.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

584×	`fma-def_binary64`
505×	`associate-l_binary64`
455×	`associate-r_binary64`
432×	`cancel-sign-sub-inv_binary64`
209×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	80	1135
1	255	844
2	878	804

Stop Event

1×	node limit

Counts

119 → 101

Calls

Call 1

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

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

prune74.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	101	5	106

Error

Counts

106 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
✓	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.5b	(.f64 (+.f64 (pow.f64 a1 2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))

Compiler

Compiled 1990 to 1301 computations (34.6% saved)

regimes690.0ms (9.7%)

Accuracy

Total 0.3b remaining (91.2%)

Threshold costs 0.3b (91.2%)

Counts

137 → 1

Compiler

Compiled 1946 to 1157 computations (40.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	16	23

Stop Event

1×

saturated

Calls

Call 1

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

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

end91.0ms (1.3%)

Stop Event

1×

fuel

Remove

(sort a1 a2)

Compiler

Compiled 156 to 110 computations (29.5% saved)

Details

analyze1.1s (14.8%)

sample4.3s (60.8%)

preprocess28.0ms (0.4%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series16.0ms (0.2%)

rewrite50.0ms (0.7%)

simplify44.0ms (0.6%)

prune101.0ms (1.4%)

localize11.0ms (0.2%)

series30.0ms (0.4%)

rewrite52.0ms (0.7%)

simplify44.0ms (0.6%)

prune131.0ms (1.8%)

localize8.0ms (0.1%)

series9.0ms (0.1%)

rewrite46.0ms (0.6%)

simplify45.0ms (0.6%)

prune147.0ms (2.1%)

localize9.0ms (0.1%)

series8.0ms (0.1%)

rewrite53.0ms (0.7%)

simplify30.0ms (0.4%)

prune74.0ms (1%)

regimes690.0ms (9.7%)

simplify2.0ms (0%)

end91.0ms (1.3%)

Profiling