Details

analyze1.1s (13.9%)

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 (55.5%)

Results

1.3s	1910×	body	1024	valid
1.0s	1523×	body	1024	invalid
867.0ms	4945×	body	128	valid
404.0ms	915×	body	512	valid
355.0ms	817×	body	512	invalid
147.0ms	481×	body	256	valid
123.0ms	414×	body	256	invalid
104.0ms	626×	body	128	invalid
5.0ms	5×	body	2048	valid

Compiler

Compiled 46 to 32 computations (30.4% saved)

preprocess30.0ms (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)))

prune5.0ms (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
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.2b	(.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))

series19.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
3.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
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)))

rewrite47.0ms (0.6%)

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)))))))

simplify42.0ms (0.5%)

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))

prune114.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	1	0	1
Picked	1	0	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 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
▶	0.4b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	15.7b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 2291 to 1473 computations (35.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series30.0ms (0.4%)

Counts

4 → 120

Calls

30 calls:

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

rewrite53.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`log-prod_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
171×	`log-pow_binary64`
113×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	229	40
2	2785	40

Stop Event

1×	node limit

Counts

4 → 129

Calls

Call 1

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

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

simplify52.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-def_binary64`
370×	`cancel-sign-sub-inv_binary64`
355×	`associate-r_binary64`
330×	`associate-/l*_binary64`
306×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	2494
1	405	2348
2	1411	1951

Stop Event

1×	node limit

Counts

249 → 193

Calls

Call 1

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

prune143.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	193	6	199

Error

Counts

199 → 6

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
	15.7b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
▶	0.4b	(.f64 (cos.f64 th) (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 3852 to 2387 computations (38% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.2b	(.f64 (cos.f64 th) (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
✓	0.4b	(*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
✓	1.0b	(/.f64 1 (neg.f64 (sqrt.f64 2)))

series6.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

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

rewrite106.0ms (1.3%)

Algorithm

3×	egg-rewrite-iter-limit
3×	egg-rewrite
1×	batch-egg-rewrite

Rules

148×	`add-sqr-sqrt_binary64`
148×	`add-sqr-sqrt_binary64`
144×	`pow1_binary64`
144×	`pow1_binary64`
142×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	45
1	309	45
2	4332	45
0	6	8
1	121	8
2	1446	8
0	6	8
0	12	16
1	249	16
2	3402	16
0	12	16
0	15	21
1	309	21
2	4337	21
0	15	21

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 25

Calls

Call 1

Inputs

(/.f64 1 (neg.f64 (sqrt.f64 2)))

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

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

Outputs

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

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

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

489×	`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	67	1313
1	198	1259
2	602	1215
3	2760	1173

Stop Event

1×	node limit

Counts

85 → 46

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 (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) (+.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)))

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

prune77.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	100	6	106

Error

Counts

106 → 6

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
▶	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
	15.7b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
✓	0.4b	(.f64 (cos.f64 th) (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 2403 to 1700 computations (29.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 a1 a2)
✓	0.2b	(.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)))
✓	0.5b	(*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))

series14.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

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

rewrite49.0ms (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)))))))))

simplify44.0ms (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))))
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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 (+.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)))

prune156.0ms (2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	215	6	221

Error

Counts

221 → 6

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cos.f64 th)) (sqrt.f64 2))
✓	0.5b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))
	0.5b	(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/2)))
	15.7b	(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
✓	0.4b	(.f64 (cos.f64 th) (.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2)))

Compiler

Compiled 4872 to 2907 computations (40.3% saved)

regimes1.2s (15.5%)

Accuracy

Total 0.5b remaining (92.7%)

Threshold costs 0.5b (92.7%)

Counts

120 → 1

Compiler

Compiled 1572 to 931 computations (40.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	12	17

Stop Event

1×

saturated

Calls

Call 1

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

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

end102.0ms (1.3%)

Stop Event

1×

fuel

Remove

(sort a1 a2)

Compiler

Compiled 151 to 118 computations (21.9% saved)

Details

analyze1.1s (13.9%)

sample4.3s (55.5%)

preprocess30.0ms (0.4%)

simplify8.0ms (0.1%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

series19.0ms (0.2%)

rewrite47.0ms (0.6%)

simplify42.0ms (0.5%)

prune114.0ms (1.5%)

localize8.0ms (0.1%)

series30.0ms (0.4%)

rewrite53.0ms (0.7%)

simplify52.0ms (0.7%)

prune143.0ms (1.8%)

localize11.0ms (0.1%)

series6.0ms (0.1%)

rewrite106.0ms (1.3%)

simplify40.0ms (0.5%)

prune77.0ms (1%)

localize11.0ms (0.1%)

series14.0ms (0.2%)

rewrite49.0ms (0.6%)

simplify44.0ms (0.6%)

prune156.0ms (2%)

regimes1.2s (15.5%)

simplify2.0ms (0%)

end102.0ms (1.3%)

Profiling