Details

analyze456.0ms (2.4%)

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

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.4s (23.2%)

Results

1.2s	1842×	body	1024	valid
1.2s	5512×	body	256	valid
925.0ms	1593×	body	1024	invalid
374.0ms	897×	body	512	valid
340.0ms	1485×	body	256	invalid
303.0ms	796×	body	512	invalid
4.0ms	5×	body	2048	valid

preprocess30.0ms (0.2%)

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

Symmetry

(sort a1 a2)

Compiler

Compiled 25 to 18 computations (28% saved)

simplify9.0ms (0%)

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)))

eval1.0ms (0%)

Compiler: Compiled 34 to 20 computations (41.2% saved)

prune2.0ms (0%)

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

1.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	1.0b	(+.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 37 to 25 computations (32.4% saved)

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))

Compiler

Compiled 37 to 16 computations (56.8% saved)

series54.0ms (0.3%)

Counts

2 → 40

Calls

12 calls:

Time	Variable		Point	Expression
42.0ms	th	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
2.0ms	th	@	-inf	(/.f64 (cos.f64 th) (sqrt.f64 2))
2.0ms	a1	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
2.0ms	th	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
1.0ms	a1	@	inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))

rewrite65.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
407×	`exp-prod_binary64`
343×	`pow-prod-down_binary64`
283×	`pow2_binary64`
198×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	224	25
2	2738	25

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (/.f64 (cos.f64 th) (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 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (pow.f64 2 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (cbrt.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (sqrt.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (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) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) 1))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (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 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (pow.f64 2 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 2)) (cbrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (sqrt.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/4) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (cbrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 2 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) 1))))))

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

821×	`unswap-sqr_binary64`
751×	`associate-l_binary64`
521×	`associate-/l/_binary64`
515×	`fma-def_binary64`
494×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	925
1	145	857
2	373	853
3	1195	821
4	4397	806

Stop Event

1×	node limit

Counts

126 → 109

Calls

Call 1

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

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

localize56.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series16.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite83.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

740×	`log-prod_binary64`
512×	`fma-def_binary64`
365×	`pow2_binary64`
251×	`pow1/3_binary64`
246×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	283	46
2	3916	45

Stop Event

1×	node limit

Counts

3 → 147

Calls

Call 1

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

Inputs

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

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

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

Outputs
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Outputs

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

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

747×	`associate-+l+_binary64`
732×	`associate-/l*_binary64`
529×	`associate-/r*_binary64`
509×	`associate-+r+_binary64`
432×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	1972
1	211	1968
2	621	1767
3	2474	1558

Stop Event

1×	node limit

Counts

231 → 178

Calls

Call 1

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

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

eval228.0ms (1.2%)

Compiler: Compiled 9104 to 5254 computations (42.3% saved)

prune128.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	380	15	395
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	382	15	397

Error

Counts

397 → 15

Alt Table

Click to see full alt table

Status	Error	Program
	0.9b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2)))
	29.1b	(.f64 (+.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (+.f64 1 (.f64 -1/2 (.f64 th th))))
	33.5b	(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
	24.7b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	24.7b	(+.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	0.9b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
▶	25.8b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
▶	1.0b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	29.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	18.7b	(.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
▶	0.7b	(fma.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) a1 (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th))))
▶	26.1b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	29.3b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
▶	1.0b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	1.0b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))

Compiler

Compiled 478 to 362 computations (24.3% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.3b	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
✓	0.5b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 58 to 31 computations (46.6% saved)

series19.0ms (0.1%)

Counts

3 → 52

Calls

15 calls:

Time	Variable		Point	Expression
5.0ms	th	@	inf	(/.f64 (sqrt.f64 2) (cos.f64 th))
2.0ms	th	@	-inf	(/.f64 (sqrt.f64 2) (cos.f64 th))
1.0ms	th	@	inf	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
1.0ms	th	@	-inf	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)
1.0ms	th	@	0	(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)

rewrite117.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`log-prod_binary64`
417×	`pow-prod-down_binary64`
326×	`pow2_binary64`
265×	`pow-unpow_binary64`
231×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	255	33
2	3407	33

Stop Event

1×	node limit

Counts

3 → 128

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (*.f64 (pow.f64 a2 4) (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 a2 4) (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))) (cbrt.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 a2) a2) (*.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 a2 (neg.f64 a2)) (/.f64 1 (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (/.f64 (*.f64 a2 a2) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 1) (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 a2 (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 a2) a2) 1) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 a2) a2) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) a2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) -2) (/.f64 (*.f64 a2 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 a2) a2) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 a2) a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 a2 a2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 a2 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 a2 a2) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) 1) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 a2 4) (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a2 -2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 a2 6) (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a2 -2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) a2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -3) (pow.f64 a2 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (cbrt.f64 a2) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 a2 a2) (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 a2 4) (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a2) (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 a2 6) (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 a2 (*.f64 a2 (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 2 (log.f64 a2) (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 2 (log.f64 a2) (log.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) a1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (cos.f64 th) a1)) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) a1) 1) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) a1) (cbrt.f64 2)) (pow.f64 2 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (*.f64 (cos.f64 th) a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (cos.f64 th)) a1) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a1 (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) a1) 2) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) a1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (*.f64 (cos.f64 th) a1) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a1)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (/.f64 1 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (pow.f64 2 1/6) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (/.f64 1 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (pow.f64 2 1/6) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) -2) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cos.f64 th) -1/2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 (pow.f64 2 1/6) (sqrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) -3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 3/2) (pow.f64 (cos.f64 th) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 2 3/2) (pow.f64 (cos.f64 th) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))))))

simplify139.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
495×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
279×	`distribute-rgt-in_binary64`
278×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	878
1	204	864
2	628	848
3	2599	814

Stop Event

1×	node limit

Counts

180 → 155

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a1 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a1 (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 a1 (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))

Outputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.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 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 -1/2 (.f64 (.f64 a2 a2) (*.f64 th th))) (sqrt.f64 2)))
(fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 th th)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(fma.f64 -1/2 (.f64 (/.f64 th (/.f64 (sqrt.f64 2) th)) (.f64 a2 a2)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (pow.f64 th 4))) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 -1/2 (.f64 (.f64 a2 a2) (.f64 th th))) (sqrt.f64 2))))
(fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (pow.f64 th 4)) (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (*.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(fma.f64 1/24 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (pow.f64 th 4)) (fma.f64 -1/2 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 th th)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (+.f64 (.f64 -1/2 (.f64 th th)) (.f64 1/24 (pow.f64 th 4)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(fma.f64 1/24 (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (pow.f64 th 4))) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (/.f64 (.f64 (.f64 a2 a2) (.f64 th th)) (sqrt.f64 2)) (.f64 -1/720 (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (pow.f64 th 6)))))))
(+.f64 (fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (pow.f64 th 4)) (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) (.f64 -1/720 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (pow.f64 th 6))))
(fma.f64 1/24 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (pow.f64 th 4)) (fma.f64 -1/2 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (.f64 th th)) (fma.f64 -1/720 (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (pow.f64 th 6)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 th (/.f64 (sqrt.f64 2) th)) (.f64 a2 a2)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2)) (.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (cos.f64 th) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(/.f64 a1 (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) a1) (sqrt.f64 2)) (/.f64 a1 (sqrt.f64 2)))
(fma.f64 -1/2 (.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 th th)) (/.f64 a1 (sqrt.f64 2)))
(fma.f64 -1/2 (.f64 (.f64 th th) (/.f64 a1 (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a1 (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) a1) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 th 4))) (/.f64 a1 (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 th th)) (fma.f64 1/24 (*.f64 (/.f64 a1 (sqrt.f64 2)) (pow.f64 th 4)) (/.f64 a1 (sqrt.f64 2))))
(fma.f64 -1/2 (.f64 (.f64 th th) (/.f64 a1 (sqrt.f64 2))) (fma.f64 1/24 (*.f64 (pow.f64 th 4) (/.f64 a1 (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2))))
(+.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 (/.f64 a1 (sqrt.f64 2)) (+.f64 (.f64 -1/2 (.f64 th th)) (.f64 1/24 (pow.f64 th 4)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 a1 (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 a1 (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 -1/720 (/.f64 (.f64 a1 (pow.f64 th 6)) (sqrt.f64 2))))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) a1) (sqrt.f64 2)) (+.f64 (fma.f64 1/24 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 th 4))) (/.f64 a1 (sqrt.f64 2))) (*.f64 -1/720 (/.f64 a1 (/.f64 (sqrt.f64 2) (pow.f64 th 6))))))
(fma.f64 -1/2 (.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 th th)) (fma.f64 1/24 (.f64 (/.f64 a1 (sqrt.f64 2)) (pow.f64 th 4)) (fma.f64 -1/720 (.f64 (/.f64 a1 (sqrt.f64 2)) (pow.f64 th 6)) (/.f64 a1 (sqrt.f64 2)))))
(fma.f64 -1/2 (.f64 (.f64 th th) (/.f64 a1 (sqrt.f64 2))) (fma.f64 1/24 (.f64 (pow.f64 th 4) (/.f64 a1 (sqrt.f64 2))) (fma.f64 -1/720 (.f64 (pow.f64 th 6) (/.f64 a1 (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2)))))
(+.f64 (fma.f64 -1/2 (.f64 (.f64 th th) (/.f64 a1 (sqrt.f64 2))) (/.f64 a1 (sqrt.f64 2))) (.f64 (/.f64 a1 (sqrt.f64 2)) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6)))))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
(*.f64 (cos.f64 th) (/.f64 a1 (sqrt.f64 2)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (*.f64 th th))))
(fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2))
(fma.f64 (.f64 th th) (.f64 (sqrt.f64 2) 1/2) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) -5/24)))))
(-.f64 (fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (.f64 -5/24 (pow.f64 th 4))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 th (.f64 th 1/2)) (.f64 (pow.f64 th 4) -5/24))))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (fma.f64 th (.f64 th 1/2) (*.f64 (pow.f64 th 4) 5/24))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (sqrt.f64 2) (fma.f64 -1 (.f64 (pow.f64 th 6) (fma.f64 -1/720 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) -5/24) (.f64 (sqrt.f64 2) 1/48)))) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (*.f64 (sqrt.f64 2) -5/24))))))
(+.f64 (sqrt.f64 2) (-.f64 (-.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) 1/2)) (.f64 (sqrt.f64 2) (.f64 -5/24 (pow.f64 th 4)))) (.f64 (pow.f64 th 6) (fma.f64 (sqrt.f64 2) -1/720 (fma.f64 (sqrt.f64 2) 1/48 (*.f64 (sqrt.f64 2) -5/48))))))
(+.f64 (sqrt.f64 2) (-.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 th (.f64 th 1/2)) (.f64 (pow.f64 th 4) -5/24))) (.f64 (pow.f64 th 6) (fma.f64 (sqrt.f64 2) -1/720 (.f64 (sqrt.f64 2) -1/12)))))
(fma.f64 (sqrt.f64 2) (fma.f64 th (.f64 th 1/2) (.f64 (pow.f64 th 4) 5/24)) (-.f64 (sqrt.f64 2) (.f64 (pow.f64 th 6) (.f64 (sqrt.f64 2) -61/720))))

localize26.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series9.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite127.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

953×	`pow1_binary64`
882×	`add-log-exp_binary64`
882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
862×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	188	31
2	2380	31

Stop Event

1×	node limit

Counts

3 → 69

Calls

Call 1

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

Outputs

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

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

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

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1035×	`unswap-sqr_binary64`
984×	`associate-*l/_binary64`
937×	`fma-def_binary64`
537×	`associate-/l*_binary64`
464×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	50	760
1	133	758
2	346	758
3	1133	732
4	3596	698
5	5174	678
6	5350	678
7	5558	678
8	5773	678
9	5977	678

Stop Event

1×	node limit

Counts

117 → 87

Calls

Call 1

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

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

localize64.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series11.0ms (0.1%)

Counts

2 → 60

Calls

15 calls:

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

rewrite117.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`prod-diff_binary64`
623×	`log-prod_binary64`
279×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	261	24
2	3622	24

Stop Event

1×	node limit

Counts

2 → 138

Calls

Call 1

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

Outputs

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

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

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

821×	`unswap-sqr_binary64`
732×	`associate-/r/_binary64`
666×	`associate-l_binary64`
555×	`associate-/l/_binary64`
456×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	1033
1	106	929
2	286	925
3	1028	893
4	3924	880

Stop Event

1×	node limit

Counts

198 → 159

Calls

Call 1

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

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

localize36.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

series7.0ms (0%)

Counts

2 → 8

Calls

12 calls:

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

rewrite76.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

921×	`pow1_binary64`
854×	`add-log-exp_binary64`
854×	`log1p-expm1-u_binary64`
854×	`expm1-log1p-u_binary64`
834×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	189	23
2	2332	23

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

940×	`distribute-rgt-out_binary64`
773×	`fma-def_binary64`
609×	`associate-*l/_binary64`
507×	`*-commutative_binary64`
477×	`associate-*r/_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	37	242
1	105	238
2	308	229
3	1192	196
4	4490	179
5	6028	162

Stop Event

1×	node limit

Counts

62 → 70

Calls

Call 1

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

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

localize32.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.4b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
✓	0.8b	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))

Compiler

Compiled 38 to 21 computations (44.7% saved)

series31.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
5.0ms	a1	@	0	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
4.0ms	a2	@	0	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
3.0ms	a1	@	0	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))
3.0ms	a1	@	inf	(/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2))
2.0ms	a2	@	inf	(pow.f64 (hypot.f64 a1 a2) 2)

rewrite75.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`log-prod_binary64`
292×	`pow2_binary64`
290×	`pow-prod-down_binary64`
204×	`pow1/3_binary64`
201×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	235	36
2	2976	36

Stop Event

1×	node limit

Counts

3 → 142

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (*.f64 (pow.f64 2 1/6) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (hypot.f64 a1 a2)) (/.f64 (pow.f64 2 1/6) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (pow.f64 2 1/6) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4)) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4)) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 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 2 (pow.f64 (hypot.f64 a1 a2) -4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 2 3/2) (pow.f64 (hypot.f64 a1 a2) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 2 3/2) (pow.f64 (hypot.f64 a1 a2) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))) 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 exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.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) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cos.f64 th)) (/.f64 1 (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (/.f64 (cos.f64 th) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))) (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))) (/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2))))))) (#(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 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (hypot.f64 a1 a2)) (hypot.f64 a1 a2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (/.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (/.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) -2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 2 1/4) (hypot.f64 a1 a2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) -2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) 1))))))

((#(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 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2))) 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) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.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)) (pow.f64 (hypot.f64 a1 a2) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 3/2) (sqrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 5) (cbrt.f64 (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.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 (pow.f64 (exp.f64 a2) a2) (exp.f64 (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 a1 a1)) (pow.f64 (exp.f64 a2) a2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (cbrt.f64 (hypot.f64 a1 a2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (hypot.f64 a1 a2)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 a1 a2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a1 a1 (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a2 a2 (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 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 (pow.f64 (cbrt.f64 a2) 2) (*.f64 (cbrt.f64 a2) a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cbrt.f64 a1) a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a2) (pow.f64 a2 3/2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 a1) (pow.f64 a1 3/2) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 a1 3/2) (sqrt.f64 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 a2 3/2) (sqrt.f64 a2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 a2) a2) (pow.f64 (cbrt.f64 a2) 2) (*.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 a1) a1) (pow.f64 (cbrt.f64 a1) 2) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a1) 5) (cbrt.f64 a1) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 a2) 5) (cbrt.f64 a2) (*.f64 a1 a1))))))

simplify97.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-in_binary64`
569×	`distribute-lft-in_binary64`
286×	`distribute-rgt-out_binary64`
257×	`fma-def_binary64`
180×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	285	3568
1	890	3189
2	3399	2757

Stop Event

1×	node limit

Counts

226 → 213

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 8))))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)))))) (pow.f64 a1 8))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)))))) (pow.f64 a1 8))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 6)) (/.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 8))))))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (pow.f64 a1 6)) (.f64 1/8 (pow.f64 a1 6)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))))) (.f64 -1 (.f64 (pow.f64 a1 2) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))))))) (pow.f64 a2 8))))))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/8 (pow.f64 a1 6)) (.f64 1/8 (pow.f64 a1 6)))) (+.f64 (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))))) (.f64 -1 (.f64 (pow.f64 a1 2) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))))))) (pow.f64 a2 8))))))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2))))))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (cos.f64 th))) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 12) (.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4)))))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))) (.f64 1/256 (/.f64 1 (pow.f64 a2 10)))))) (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (cos.f64 th))) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (.f64 (cos.f64 th) (pow.f64 a2 8))) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (.f64 (pow.f64 a2 8) (cos.f64 th))) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a1 8))) (.f64 -1/2 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 2)))) (pow.f64 a1 2))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4))) (+.f64 (.f64 1/256 (/.f64 1 (pow.f64 a1 10))) (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a1 8))) (.f64 -1/2 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 2)))) (pow.f64 a1 2))) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a1 5)) 2) (.f64 1/8 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4))))))))) (.f64 (cos.f64 th) (pow.f64 a2 12))) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2))))))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a1 8)) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (pow.f64 a2 8)) (pow.f64 a1 2)))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))

Outputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (.f64 a2 a2)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 a2 4)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 4)) (*.f64 a1 a1)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 a2 4))) (/.f64 (pow.f64 a1 4) (/.f64 (pow.f64 a2 6) (sqrt.f64 2))))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (-.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 4)) (.f64 a1 a1))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 8))))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (neg.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 8) (pow.f64 a1 6)))))))
(-.f64 (+.f64 (/.f64 (pow.f64 a1 4) (/.f64 (pow.f64 a2 6) (sqrt.f64 2))) (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 8) (pow.f64 a1 6))))) (/.f64 (.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 a2 4)))
(+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)) (-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (.f64 (/.f64 (pow.f64 a1 6) (pow.f64 a2 8)) (sqrt.f64 2))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 4)) (*.f64 a1 a1))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(fma.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (.f64 a2 a2)) (pow.f64 a1 4)) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
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(fma.f64 (pow.f64 a1 8) (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (fma.f64 a2 a2 (*.f64 a1 a1)))
(fma.f64 (pow.f64 a1 8) (+.f64 (neg.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (.f64 (/.f64 1 (pow.f64 a2 6)) 1/64)) (fma.f64 a2 a2 (.f64 a1 a1)))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (/.f64 (pow.f64 a2 4) a1) (/.f64 1/4 a1)))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (/.f64 (pow.f64 a2 6) (/.f64 (pow.f64 a1 4) 1/8)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (*.f64 (/.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 6)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (/.f64 (pow.f64 a2 4) a1) (/.f64 1/4 a1)))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (/.f64 (pow.f64 a2 6) (/.f64 (pow.f64 a1 4) 1/8)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (*.f64 (/.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 6)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (pow.f64 a2 8)) (pow.f64 a1 2)))
(+.f64 (.f64 a2 a2) (fma.f64 (fma.f64 -1 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (/.f64 5/64 (pow.f64 a1 6))) (pow.f64 a2 8) (.f64 a1 a1)))
(fma.f64 a2 a2 (fma.f64 (pow.f64 a2 8) (-.f64 (/.f64 5/64 (pow.f64 a1 6)) (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (*.f64 a1 a1)))
(fma.f64 a2 a2 (fma.f64 (pow.f64 a2 8) (-.f64 (.f64 (/.f64 1 (pow.f64 a1 6)) 1/64) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (.f64 a1 a1)))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))

eval394.0ms (2.1%)

Compiler: Compiled 16719 to 10236 computations (38.8% saved)

prune192.0ms (1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	773	19	792
Fresh	8	2	10
Picked	1	0	1
Done	3	1	4
Total	785	22	807

Error

Counts

807 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	0.9b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
▶	29.5b	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
▶	29.3b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.8b	(/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 2))
	43.8b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	29.5b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	26.0b	(.f64 (cos.f64 th) (.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))
	29.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	25.8b	(*.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1)))
	26.1b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	24.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	0.8b	(*.f64 (pow.f64 2 -1/2) (/.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) -2)))
	29.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
▶	0.6b	(/.f64 (cos.f64 th) (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)))
	26.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	39.1b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
✓	25.8b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
▶	39.1b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	29.3b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
	1.0b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	26.0b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
▶	25.7b	(.f64 (pow.f64 2 -1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 552 to 417 computations (24.5% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 39 to 22 computations (43.6% saved)

series13.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite139.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
311×	`pow2_binary64`
307×	`pow-prod-down_binary64`
216×	`pow1/3_binary64`
214×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	251	36
2	3015	36

Stop Event

1×	node limit

Counts

3 → 97

Calls

Call 1

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

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.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 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 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 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (sqrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (cos.f64 th)) (/.f64 1 (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (neg.f64 (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 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 (hypot.f64 a1 a2) -2)) (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 -1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (/.f64 (cbrt.f64 (cos.f64 th)) (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (/.f64 (sqrt.f64 (cos.f64 th)) (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (/.f64 (cos.f64 th) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)) -1/2) (/.f64 (cos.f64 th) (*.f64 (pow.f64 2 1/4) (/.f64 1 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (*.f64 (pow.f64 2 1/4) (/.f64 1 (hypot.f64 a1 a2)))) (/.f64 (cbrt.f64 (cos.f64 th)) (*.f64 (pow.f64 2 1/4) (/.f64 1 (hypot.f64 a1 a2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (cos.f64 th) (/.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 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) -2) (/.f64 (cos.f64 th) (sqrt.f64 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 (pow.f64 2 3/2) (pow.f64 (hypot.f64 a1 a2) -6))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) -2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (cos.f64 th) (*.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 (cos.f64 th) 2) (*.f64 2 (pow.f64 (hypot.f64 a1 a2) -4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (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 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (cos.f64 th) 3) (*.f64 (pow.f64 2 3/2) (pow.f64 (hypot.f64 a1 a2) -6))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) -2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1) 1))))))

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

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

619×	`distribute-rgt-in_binary64`
599×	`distribute-lft-in_binary64`
296×	`distribute-rgt-out_binary64`
287×	`fma-def_binary64`
200×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	3944
1	1008	3549
2	3869	3151

Stop Event

1×	node limit

Counts

181 → 175

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 8))))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)))))) (pow.f64 a1 8))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
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(+.f64 (.f64 -1 (/.f64 (pow.f64 a2 6) (pow.f64 a1 8))) (+.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)) (+.f64 (.f64 -1 (/.f64 (pow.f64 a2 2) (pow.f64 a1 4))) (/.f64 1 (pow.f64 a1 2)))))
(/.f64 1 (pow.f64 a2 2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (/.f64 1 (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2)))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4)))) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))))) (.f64 1/8 (pow.f64 a1 6))) (pow.f64 a2 8))) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a1 2)) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2))))))))
(/.f64 1 (pow.f64 a2 2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (/.f64 1 (pow.f64 a2 2)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2)))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4)))) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))))) (.f64 1/8 (pow.f64 a1 6))) (pow.f64 a2 8))) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a1 2)) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2))))))))

Outputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (.f64 a2 a2)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 a2 4)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (.f64 (sqrt.f64 2) (.f64 a1 a1)) (pow.f64 a2 4))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)))
(+.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (-.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (*.f64 a1 a1)))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 8))))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)) (pow.f64 a2 6)) (+.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (neg.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 8) (pow.f64 a1 6)))))))
(-.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)) (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (pow.f64 a1 6) (/.f64 (pow.f64 a2 8) (sqrt.f64 2))))) (/.f64 (.f64 (sqrt.f64 2) (.f64 a1 a1)) (pow.f64 a2 4)))
(+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 4)) (-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 8) (pow.f64 a1 6)))) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (*.f64 a1 a1)))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (.f64 a1 a1)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6)))))
(+.f64 (fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2))) (/.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (*.f64 (sqrt.f64 2) (pow.f64 a2 4))) (pow.f64 a1 6)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2))) (/.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))) (pow.f64 a1 6)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)))))) (pow.f64 a1 8))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (fma.f64 -1 (/.f64 (fma.f64 -1 (.f64 (.f64 a2 a2) (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4))))) (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 6) 0) (neg.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (.f64 (pow.f64 a2 4) 0)))))) (pow.f64 a1 8)) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(-.f64 (-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (pow.f64 a1 6))) (/.f64 (fma.f64 (neg.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (.f64 a2 a2) (fma.f64 (sqrt.f64 2) 0 (.f64 (sqrt.f64 2) 0))) (pow.f64 a1 8))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))) (pow.f64 a1 6))) (+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2)) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))))) (pow.f64 a1 8))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (.f64 a1 a1)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6)))))
(+.f64 (fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2))) (/.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (*.f64 (sqrt.f64 2) (pow.f64 a2 4))) (pow.f64 a1 6)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2))) (/.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))) (pow.f64 a1 6)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a2 2))) (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6)))) (.f64 -1 (.f64 (sqrt.f64 2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)))))) (pow.f64 a1 8))) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (fma.f64 -1 (/.f64 (fma.f64 -1 (.f64 (.f64 a2 a2) (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4))))) (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 6) 0) (neg.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 a2 a2) (.f64 (pow.f64 a2 4) 0)))))) (pow.f64 a1 8)) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (neg.f64 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a2 4) 0) (neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (pow.f64 a1 6))))))
(-.f64 (-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (pow.f64 a1 6))) (/.f64 (fma.f64 (neg.f64 (-.f64 (.f64 (sqrt.f64 2) 0) (.f64 (sqrt.f64 2) (pow.f64 a2 4)))) (.f64 a2 a2) (fma.f64 (sqrt.f64 2) 0 (.f64 (sqrt.f64 2) 0))) (pow.f64 a1 8))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))) (pow.f64 a1 6))) (+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2)) (/.f64 (.f64 (.f64 a2 a2) (neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 4))))) (pow.f64 a1 8))))
(/.f64 (sqrt.f64 2) (pow.f64 a1 2))
(/.f64 (sqrt.f64 2) (*.f64 a1 a1))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (/.f64 (sqrt.f64 2) (pow.f64 a1 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (.f64 a1 a1)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 6)) (/.f64 (sqrt.f64 2) (pow.f64 a1 2))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))))
(-.f64 (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 4))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (.f64 a2 a2))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 4)))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 2)) (pow.f64 a1 4))) (+.f64 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 4)) (pow.f64 a1 6)) (+.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 2)) (.f64 -1 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 6)) (pow.f64 a1 8))))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 4) (.f64 a2 a2))) (+.f64 (+.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)))) (neg.f64 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a1 8) (pow.f64 a2 6))))))
(-.f64 (+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 4)) (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 8)) (pow.f64 a2 6)))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2)))
(+.f64 (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 6)) (pow.f64 a2 4)) (-.f64 (-.f64 (/.f64 (sqrt.f64 2) (.f64 a1 a1)) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 8)) (pow.f64 a2 6))) (.f64 (/.f64 (sqrt.f64 2) (pow.f64 a1 4)) (*.f64 a2 a2))))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2)))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (.f64 a2 a2)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (.f64 (sqrt.f64 2) (*.f64 a1 a1)) (pow.f64 a2 4)))
(-.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))))
(+.f64 (.f64 -1 (/.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 2)) (pow.f64 a2 4))) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 (sqrt.f64 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6))) (/.f64 (sqrt.f64 2) (pow.f64 a2 2))))
(fma.f64 -1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 a2 4) (.f64 a1 a1))) (fma.f64 -1 (/.f64 (fma.f64 (sqrt.f64 2) (.f64 (pow.f64 a1 4) 0) (neg.f64 (.f64 (sqrt.f64 2) (pow.f64 a1 4)))) (pow.f64 a2 6)) (/.f64 (sqrt.f64 2) (.f64 a2 a2))))
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(/.f64 1 (pow.f64 a1 2))
(/.f64 1 (*.f64 a1 a1))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 a2 2) (pow.f64 a1 4))) (/.f64 1 (pow.f64 a1 2)))
(fma.f64 -1 (/.f64 (.f64 a2 a2) (pow.f64 a1 4)) (/.f64 1 (.f64 a1 a1)))
(-.f64 (/.f64 1 (*.f64 a1 a1)) (/.f64 a2 (/.f64 (pow.f64 a1 4) a2)))
(+.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)) (+.f64 (*.f64 -1 (/.f64 (pow.f64 a2 2) (pow.f64 a1 4))) (/.f64 1 (pow.f64 a1 2))))
(+.f64 (fma.f64 -1 (/.f64 (.f64 a2 a2) (pow.f64 a1 4)) (/.f64 1 (.f64 a1 a1))) (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)))
(+.f64 (-.f64 (/.f64 1 (*.f64 a1 a1)) (/.f64 a2 (/.f64 (pow.f64 a1 4) a2))) (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)))
(+.f64 (/.f64 1 (*.f64 a1 a1)) (-.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)) (/.f64 a2 (/.f64 (pow.f64 a1 4) a2))))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a2 6) (pow.f64 a1 8))) (+.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)) (+.f64 (.f64 -1 (/.f64 (pow.f64 a2 2) (pow.f64 a1 4))) (/.f64 1 (pow.f64 a1 2)))))
(fma.f64 -1 (/.f64 (pow.f64 a2 6) (pow.f64 a1 8)) (+.f64 (fma.f64 -1 (/.f64 (.f64 a2 a2) (pow.f64 a1 4)) (/.f64 1 (.f64 a1 a1))) (/.f64 (pow.f64 a2 4) (pow.f64 a1 6))))
(-.f64 (+.f64 (-.f64 (/.f64 1 (*.f64 a1 a1)) (/.f64 a2 (/.f64 (pow.f64 a1 4) a2))) (/.f64 (pow.f64 a2 4) (pow.f64 a1 6))) (/.f64 (pow.f64 a2 6) (pow.f64 a1 8)))
(+.f64 (/.f64 (pow.f64 a2 4) (pow.f64 a1 6)) (-.f64 (-.f64 (/.f64 1 (*.f64 a1 a1)) (/.f64 a2 (/.f64 (pow.f64 a1 4) a2))) (/.f64 (pow.f64 a2 6) (pow.f64 a1 8))))
(/.f64 1 (pow.f64 a2 2))
(/.f64 1 (*.f64 a2 a2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (/.f64 1 (pow.f64 a2 2)))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (/.f64 1 (.f64 a2 a2)))
(-.f64 (/.f64 1 (.f64 a2 a2)) (/.f64 (.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (/.f64 1 (*.f64 a2 a2)) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2)))))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (*.f64 a2 a2)))))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2)))) (/.f64 (*.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2)))) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4)))) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))))) (.f64 1/8 (pow.f64 a1 6))) (pow.f64 a2 8))) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a1 2)) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2))))))))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) -3/8))) (fma.f64 -2 (/.f64 (fma.f64 -1/2 (.f64 (.f64 a1 a1) (.f64 (pow.f64 a1 4) -3/8)) (.f64 (pow.f64 a1 6) 1/8)) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) -3/8))) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (*.f64 a2 a2))))))))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (fma.f64 (pow.f64 a1 6) 1/8 (.f64 -1/2 (.f64 (pow.f64 a1 6) -3/8))) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2))))))) (/.f64 (*.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 a1 6) -3/8) (.f64 (pow.f64 a1 6) 1/8)) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2))))))) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))
(/.f64 1 (pow.f64 a2 2))
(/.f64 1 (*.f64 a2 a2))
(+.f64 (*.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (/.f64 1 (pow.f64 a2 2)))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (/.f64 1 (.f64 a2 a2)))
(-.f64 (/.f64 1 (.f64 a2 a2)) (/.f64 (.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (/.f64 1 (*.f64 a2 a2)) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2)))))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (*.f64 a2 a2)))))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2)))) (/.f64 (*.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2)))) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))
(+.f64 (.f64 -1 (/.f64 (pow.f64 a1 2) (pow.f64 a2 4))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4)))) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))))) (.f64 1/8 (pow.f64 a1 6))) (pow.f64 a2 8))) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a1 2)) (pow.f64 a2 8))) (+.f64 (.f64 -2 (/.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (*.f64 -1/8 (pow.f64 a1 4))) (pow.f64 a2 6))) (/.f64 1 (pow.f64 a2 2))))))))
(fma.f64 -1 (/.f64 (.f64 a1 a1) (pow.f64 a2 4)) (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) -3/8))) (fma.f64 -2 (/.f64 (fma.f64 -1/2 (.f64 (.f64 a1 a1) (.f64 (pow.f64 a1 4) -3/8)) (.f64 (pow.f64 a1 6) 1/8)) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 a1 a1) (/.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) -3/8))) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (*.f64 a2 a2))))))))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (fma.f64 (pow.f64 a1 6) 1/8 (.f64 -1/2 (.f64 (pow.f64 a1 6) -3/8))) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2))))))) (/.f64 (*.f64 a1 a1) (pow.f64 a2 4)))
(-.f64 (fma.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 6)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (fma.f64 -1/2 (.f64 (pow.f64 a1 6) -3/8) (.f64 (pow.f64 a1 6) 1/8)) (pow.f64 a2 8)) (fma.f64 1/2 (/.f64 (.f64 (pow.f64 a1 6) -3/8) (pow.f64 a2 8)) (fma.f64 -2 (/.f64 (.f64 (pow.f64 a1 4) -3/8) (pow.f64 a2 6)) (/.f64 1 (.f64 a2 a2))))))) (/.f64 a1 (/.f64 (pow.f64 a2 4) a1)))

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
576×	`add-log-exp_binary64`
576×	`log1p-expm1-u_binary64`
576×	`expm1-log1p-u_binary64`
564×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	127	9
2	1566	9

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

759×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
423×	`*-commutative_binary64`
423×	`associate-*r/_binary64`
393×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	108
1	11	108
2	20	108
3	37	108
4	83	108
5	266	108
6	1091	108
7	3478	108
8	4280	108
9	4465	108
10	4681	108
11	5028	108
12	5456	108
13	5935	108
14	6584	108
15	7273	108

Stop Event

1×	node limit

Counts

32 → 22

Calls

Call 1

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

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

localize63.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series14.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
7.0ms	a2	@	0	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms	th	@	inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms	th	@	-inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms	th	@	0	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms	a2	@	inf	(/.f64 a2 (sqrt.f64 2))

rewrite104.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

953×	`pow1_binary64`
882×	`add-log-exp_binary64`
882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
862×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	188	31
2	2380	31

Stop Event

1×	node limit

Counts

3 → 69

Calls

Call 1

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

Outputs

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

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

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

simplify156.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1035×	`unswap-sqr_binary64`
985×	`associate-*l/_binary64`
967×	`fma-def_binary64`
537×	`associate-/l*_binary64`
469×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	53	764
1	135	760
2	350	758
3	1142	732
4	3628	698
5	5294	678
6	5470	678
7	5679	678
8	5894	678
9	6098	678

Stop Event

1×	node limit

Counts

117 → 89

Calls

Call 1

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

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

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 15 computations (46.4% saved)

series3.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite85.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

928×	`pow1_binary64`
860×	`add-log-exp_binary64`
860×	`log1p-expm1-u_binary64`
860×	`expm1-log1p-u_binary64`
839×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	187	23
2	2357	23

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

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

Outputs

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

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

simplify107.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1182×	`unswap-sqr_binary64`
731×	`associate-*l/_binary64`
623×	`fma-def_binary64`
541×	`associate-*r/_binary64`
384×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	34	538
1	82	534
2	228	532
3	872	514
4	2813	495
5	4554	483
6	6013	483
7	6315	483
8	6543	483
9	6749	483

Stop Event

1×	node limit

Counts

94 → 69

Calls

Call 1

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

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

localize25.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 32 to 15 computations (53.1% saved)

series7.0ms (0%)

Counts

3 → 52

Calls

18 calls:

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

rewrite94.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

933×	`pow1_binary64`
861×	`add-log-exp_binary64`
860×	`log1p-expm1-u_binary64`
860×	`expm1-log1p-u_binary64`
842×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	207	29
2	2390	29

Stop Event

1×	node limit

Counts

3 → 39

Calls

Call 1

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

Outputs

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

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

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

simplify265.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

897×	`distribute-lft-out_binary64`
697×	`sqr-pow_binary64`
681×	`*-commutative_binary64`
408×	`fma-def_binary64`
386×	`+-commutative_binary64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	52	772
1	150	766
2	451	725
3	1858	704
4	3463	698
5	3718	698
6	3915	698
7	4103	698
8	4343	698
9	4622	696
10	6066	696
11	6370	696
12	6713	696
13	7123	696
14	7604	696

Stop Event

1×	node limit

Counts

91 → 66

Calls

Call 1

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

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

eval220.0ms (1.2%)

Compiler: Compiled 8570 to 5889 computations (31.3% saved)

prune110.0ms (0.6%)

Pruning

27 alts after pruning (25 fresh and 2 done)

	Pruned	Kept	Total
New	434	18	452
Fresh	9	7	16
Picked	0	1	1
Done	4	1	5
Total	447	27	474

Error

Counts

474 → 27

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.9b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	39.1b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	29.3b	(.f64 a2 (.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
	45.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
▶	44.1b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
	39.2b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	43.8b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	26.0b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
	29.3b	(/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2))
	39.1b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	43.5b	(/.f64 (.f64 (+.f64 1 (.f64 th (.f64 th -1/2))) (.f64 a2 a2)) (sqrt.f64 2))
	44.3b	(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
✓	39.1b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	1.0b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	29.5b	(.f64 (.f64 (pow.f64 2 -1/2) (*.f64 a2 a2)) (cos.f64 th))
	26.0b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
	53.3b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	29.7b	(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 (.f64 a2 (cos.f64 th)))))
	29.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
▶	25.8b	(*.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1)))
	29.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	24.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	29.5b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	40.0b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	39.1b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	29.5b	(.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (cos.f64 th))
✓	25.7b	(.f64 (pow.f64 2 -1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 660 to 503 computations (23.8% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	0.2b	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
✓	0.8b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 46 to 21 computations (54.3% saved)

series6.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite74.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

961×	`prod-diff_binary64`
636×	`log-prod_binary64`
298×	`fma-def_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	281	25
2	3633	25

Stop Event

1×	node limit

Counts

2 → 85

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 3)) (fma.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))) (-.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (exp.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a2 (*.f64 a2 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a1 (*.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 a1 4)) (*.f64 (pow.f64 (cbrt.f64 a1) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 a2 4)) (*.f64 (pow.f64 (cbrt.f64 a2) 2) (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2)) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 a1 a1)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 a1 a1)) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))) (cbrt.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))) (cbrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (sqrt.f64 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1)))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) a2) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) a2) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a2 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (*.f64 a2 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) a1) (*.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) a1) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 a1 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (*.f64 a1 (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a2 a2) (cos.f64 th)) (sqrt.f64 1/2) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a1 a1) (cos.f64 th)) (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) a2) a2 (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (cbrt.f64 (pow.f64 a2 4))) (pow.f64 (cbrt.f64 a2) 2) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a2 a2) (sqrt.f64 1/2)) (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a2 a2) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))) (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a2 a2) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (sqrt.f64 1/2) (*.f64 (cos.f64 th) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) a1) a1 (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (cbrt.f64 (pow.f64 a1 4))) (pow.f64 (cbrt.f64 a1) 2) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a1 a1) (sqrt.f64 1/2)) (cos.f64 th) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a1 a1) (cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 2) 1/2))) (cbrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 a1 a1) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)))) (sqrt.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th))) (*.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))))))

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

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

837×	`distribute-rgt-in_binary64`
820×	`distribute-lft-in_binary64`
502×	`distribute-lft-out_binary64`
488×	`unswap-sqr_binary64`
450×	`associate-+l+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	958
1	148	884
2	437	838
3	1878	810
4	5156	806

Stop Event

1×	node limit

Counts

133 → 108

Calls

Call 1

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

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

localize10.0ms (0%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
576×	`add-log-exp_binary64`
576×	`log1p-expm1-u_binary64`
576×	`expm1-log1p-u_binary64`
564×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	127	9
2	1566	9

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

759×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
423×	`*-commutative_binary64`
423×	`associate-*r/_binary64`
393×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	108
1	11	108
2	20	108
3	37	108
4	83	108
5	266	108
6	1091	108
7	3478	108
8	4280	108
9	4465	108
10	4681	108
11	5028	108
12	5456	108
13	5935	108
14	6584	108
15	7273	108

Stop Event

1×	node limit

Counts

32 → 22

Calls

Call 1

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

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

localize48.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 a1 (sqrt.f64 2)))
✓	0.1b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
	0.4b	(/.f64 a1 (sqrt.f64 2))
✓	3.7b	(-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1)

Compiler

Compiled 36 to 30 computations (16.7% saved)

series3.0ms (0%)

Counts

3 → 27

Calls

9 calls:

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

rewrite122.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

991×	`pow1_binary64`
931×	`add-log-exp_binary64`
930×	`log1p-expm1-u_binary64`
930×	`expm1-log1p-u_binary64`
102×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	202	23
2	2822	23

Stop Event

1×	node limit

Counts

3 → 121

Calls

Call 1

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

Outputs

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

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

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

simplify167.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

760×	`sqr-pow_binary64`
444×	`associate-*r/_binary64`
434×	`unswap-sqr_binary64`
415×	`*-commutative_binary64`
393×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	193
1	14	193
2	21	193
3	38	193
4	86	193
5	274	193
6	1103	193
7	3496	193
8	4318	193
9	4503	193
10	4719	193
11	5069	193
12	5499	193
13	5982	193
14	6634	193
15	7323	193

Stop Event

1×	node limit

Counts

148 → 124

Calls

Call 1

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

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

localize27.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1)))
✓	0.3b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))
✓	0.4b	(/.f64 (sqrt.f64 2) a1)

Compiler

Compiled 30 to 19 computations (36.7% saved)

series8.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite105.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`log-prod_binary64`
408×	`exp-prod_binary64`
287×	`pow-prod-down_binary64`
252×	`pow2_binary64`
210×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	194	31
2	2630	31

Stop Event

1×	node limit

Counts

3 → 152

Calls

Call 1

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

Outputs

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

simplify115.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1035×	`unswap-sqr_binary64`
984×	`associate-*l/_binary64`
937×	`fma-def_binary64`
537×	`associate-/l*_binary64`
460×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	50	760
1	133	758
2	346	758
3	1134	732
4	3592	698
5	5170	678
6	5346	678
7	5554	678
8	5769	678
9	5973	678

Stop Event

1×	node limit

Counts

200 → 171

Calls

Call 1

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

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

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
	0.5b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Compiler

Compiled 27 to 15 computations (44.4% saved)

eval379.0ms (2%)

Compiler: Compiled 10343 to 6682 computations (35.4% saved)

prune162.0ms (0.8%)

Pruning

36 alts after pruning (30 fresh and 6 done)

	Pruned	Kept	Total
New	648	15	663
Fresh	5	15	20
Picked	0	1	1
Done	1	5	6
Total	654	36	690

Error

Counts

690 → 36

Alt Table

Click to see full alt table

Status	Error	Program
✓	40.0b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	0.9b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	39.1b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	53.3b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	29.3b	(/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2))
	40.1b	(.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2)))
	45.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
✓	44.1b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
	39.2b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	43.8b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	26.0b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
	39.1b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	40.0b	(.f64 a2 (.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	43.5b	(/.f64 (.f64 (+.f64 1 (.f64 th (.f64 th -1/2))) (.f64 a2 a2)) (sqrt.f64 2))
	44.3b	(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
✓	39.1b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	40.0b	(.f64 a2 (.f64 (pow.f64 2 -1/2) a2))
	29.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a2 a2))
	29.5b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	54.5b	(*.f64 a1 (-.f64 1 1))
	26.0b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
	44.3b	(*.f64 a2 (-.f64 (+.f64 1 (/.f64 a2 (sqrt.f64 2))) 1))
	29.7b	(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 (.f64 a2 (cos.f64 th)))))
	40.0b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	29.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
✓	25.8b	(*.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1)))
	29.6b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	40.0b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	24.8b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	29.5b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	44.7b	(-.f64 (+.f64 1 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1)
	39.1b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	24.7b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	53.9b	(.f64 a1 (-.f64 (+.f64 1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2))) 1))
	40.0b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	25.7b	(.f64 (pow.f64 2 -1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 436 to 338 computations (22.5% saved)

regimes540.0ms (2.8%)

Counts

69 → 1

Calls

Call 1

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

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

Calls

11 calls:

83.0ms	th
62.0ms	(*.f64 a1 a1)
53.0ms	(*.f64 a2 a2)
50.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
47.0ms	a1

Results

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

Compiler

Compiled 792 to 460 computations (41.9% saved)

regimes953.0ms (5%)

Counts

60 → 1

Calls

Call 1

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

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

Calls

8 calls:

682.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
44.0ms	(cos.f64 th)
41.0ms	a1
38.0ms	th
36.0ms	a2

Results

Error	Segments	Branch
0.9b	1	`a1`
0.9b	1	`a2`
0.9b	1	`th`
0.9b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.9b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.9b	1	`(cos.f64 th)`
0.9b	1	`(*.f64 a1 a1)`
0.9b	1	`(*.f64 a2 a2)`

Compiler

Compiled 627 to 361 computations (42.4% saved)

regimes1.8s (9.7%)

Counts

50 → 2

Calls

Call 1

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

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

Calls

10 calls:

397.0ms	th
356.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
317.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
252.0ms	(cos.f64 th)
123.0ms	a2

Results

Error	Segments	Branch
4.9b	2	`a1`
7.0b	4	`a2`
6.1b	10	`th`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(cos.f64 th)`
8.4b	5	`(*.f64 a1 a1)`
8.4b	5	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 509 to 306 computations (39.9% saved)

bsearch59.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	-2.7561877992818123e-146	-3.569504602840413e-153

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes1.6s (8.5%)

Counts

48 → 2

Calls

Call 1

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

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

Calls

10 calls:

374.0ms	th
243.0ms	a2
181.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
176.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
167.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
4.9b	2	`a1`
7.1b	4	`a2`
6.1b	10	`th`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(cos.f64 th)`
8.4b	5	`(*.f64 a1 a1)`
8.4b	5	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 488 to 294 computations (39.8% saved)

bsearch66.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
66.0ms	-2.7561877992818123e-146	-3.569504602840413e-153

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes709.0ms (3.7%)

Counts

36 → 2

Calls

Call 1

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

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

Calls

10 calls:

188.0ms	th
73.0ms	a2
71.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
71.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
67.0ms	(cos.f64 th)

Results

Error	Segments	Branch
5.0b	2	`a1`
7.1b	4	`a2`
6.2b	10	`th`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.8b	5	`(cos.f64 th)`
8.4b	5	`(*.f64 a1 a1)`
8.4b	5	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 376 to 238 computations (36.7% saved)

bsearch61.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
61.0ms	-2.7561877992818123e-146	-3.569504602840413e-153

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes415.0ms (2.2%)

Counts

34 → 2

Calls

Call 1

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

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

Calls

7 calls:

126.0ms	th
65.0ms	a2
60.0ms	(cos.f64 th)
41.0ms	(*.f64 a1 a1)
40.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
5.1b	2	`a1`
7.3b	4	`a2`
7.3b	8	`th`
10.1b	5	`(cos.f64 th)`
8.6b	5	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 336 to 211 computations (37.2% saved)

bsearch59.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	-2.7561877992818123e-146	-3.569504602840413e-153

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes324.0ms (1.7%)

Counts

28 → 2

Calls

Call 1

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

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

Calls

6 calls:

110.0ms	th
55.0ms	a2
52.0ms	(cos.f64 th)
34.0ms	(*.f64 a1 a1)
34.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
5.4b	2	`a1`
7.6b	4	`a2`
7.4b	8	`th`
10.1b	5	`(cos.f64 th)`
8.9b	5	`(*.f64 a1 a1)`
10.0b	4	`(*.f64 a2 a2)`

Compiler

Compiled 276 to 180 computations (34.8% saved)

bsearch60.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	-2.7561877992818123e-146	-3.569504602840413e-153

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes189.0ms (1%)

Counts

27 → 2

Calls

Call 1

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

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

Calls

6 calls:

41.0ms	a2
40.0ms	th
35.0ms	(*.f64 a2 a2)
26.0ms	a1
23.0ms	(cos.f64 th)

Results

Error	Segments	Branch
15.9b	2	`a1`
17.4b	2	`a2`
15.1b	3	`th`
15.1b	2	`(cos.f64 th)`
17.4b	2	`(*.f64 a1 a1)`
18.4b	4	`(*.f64 a2 a2)`

Compiler

Compiled 267 to 176 computations (34.1% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9952775961793049	0.9981807128361507

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes141.0ms (0.7%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

5 calls:

31.0ms	th
30.0ms	a1
30.0ms	a2
17.0ms	(*.f64 a1 a1)
17.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
24.7b	1	`a1`
24.7b	1	`a2`
24.7b	1	`th`
24.7b	1	`(*.f64 a1 a1)`
24.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 253 to 167 computations (34% saved)

regimes310.0ms (1.6%)

Counts

18 → 4

Calls

Call 1

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

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

Calls

6 calls:

78.0ms	th
74.0ms	a2
42.0ms	(*.f64 a2 a2)
42.0ms	(*.f64 a2 a2)
40.0ms	a1

Results

Error	Segments	Branch
27.1b	2	`a1`
26.9b	4	`a2`
36.1b	3	`th`
29.7b	2	`(*.f64 a1 a1)`
28.6b	4	`(*.f64 a2 a2)`
28.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 163 to 109 computations (33.1% saved)

bsearch224.0ms (1.2%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
58.0ms	1.4614409330228602e-45	5.5501042921593084e-42
57.0ms	7.783531299346684e-70	1.784630356774731e-67
109.0ms	1.9566498730172507e-159	1.55704422492915e-158

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes113.0ms (0.6%)

Counts

11 → 4

Calls

Call 1

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

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

Calls

6 calls:

27.0ms	th
26.0ms	a2
19.0ms	(*.f64 a2 a2)
15.0ms	(*.f64 a2 a2)
13.0ms	a1

Results

Error	Segments	Branch
27.1b	2	`a1`
27.0b	4	`a2`
36.1b	3	`th`
29.7b	2	`(*.f64 a1 a1)`
28.6b	4	`(*.f64 a2 a2)`
28.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 101 to 67 computations (33.7% saved)

bsearch177.0ms (0.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
57.0ms	1.4614409330228602e-45	5.5501042921593084e-42
57.0ms	7.783531299346684e-70	1.784630356774731e-67
62.0ms	1.9566498730172507e-159	1.55704422492915e-158

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes64.0ms (0.3%)

Counts

5 → 4

Calls

Call 1

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

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

Calls

5 calls:

18.0ms	a2
17.0ms	th
11.0ms	(*.f64 a2 a2)
8.0ms	a1
8.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.1b	2	`a1`
27.0b	4	`a2`
36.1b	3	`th`
29.7b	2	`(*.f64 a1 a1)`
28.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 56 to 40 computations (28.6% saved)

bsearch178.0ms (0.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
59.0ms	1.4614409330228602e-45	5.5501042921593084e-42
59.0ms	7.783531299346684e-70	1.784630356774731e-67
59.0ms	1.9566498730172507e-159	1.55704422492915e-158

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes16.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

4.0ms	th
4.0ms	a2
4.0ms	a1
3.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
40.0b	1	`a1`
40.0b	1	`a2`
40.0b	1	`th`
40.0b	1	`(*.f64 a2 a2)`

Compiler

Compiled 38 to 28 computations (26.3% saved)

regimes12.0ms (0.1%)

Accuracy

Total -14.7b remaining (-36.8%)

Threshold costs -14.7b (-36.8%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	a1
3.0ms	a2
3.0ms	th

Results

Error	Segments	Branch
40.0b	1	`a1`
40.0b	1	`a2`
40.0b	1	`th`

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	450
1	91	450

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (cos.f64 th) (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (pow.f64 2 -1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 2242792614430507/2251799813685248) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2))) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2))))))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a1 (-.f64 1 1))

Outputs
(/.f64 (cos.f64 th) (*.f64 (pow.f64 (hypot.f64 a1 a2) -2) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (pow.f64 2 -1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (pow.f64 2 -1/2) (.f64 a1 (.f64 (cos.f64 th) a1))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 a1 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a1))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (/.f64 (.f64 (.f64 a1 (cos.f64 th)) a1) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (/.f64 (.f64 a1 (.f64 (cos.f64 th) a1)) (sqrt.f64 2)) (/.f64 (*.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (/.f64 (.f64 (cos.f64 th) a2) (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -1549981413817575/56236422431789954785131731346074773235871213978773957913759444657647969758393598378988008576298635714374011382919011189040103325693678746112606439760814548189184) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 2242792614430507/2251799813685248) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2))) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2))))))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(if (<=.f64 a2 3871511989085245/1978643211784836272484020168157177520281050792809694719312504448743177800852254937362531208489944359916781371408129114714810920274454009679740369240815145343332854177189593088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (if (<=.f64 a2 6048329650762445/7770675568902916283677847627294075626569627356208558085007249638955617140820833992704) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (if (<=.f64 a2 2348445034711789/1606938044258990275541962092341162602522202993782792835301376) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a1 (-.f64 1 1))
(*.f64 a1 0)

Compiler

Compiled 341 to 235 computations (31.1% saved)

soundness11.0ms (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

Compiler

Compiled 53 to 36 computations (32.1% saved)

end149.0ms (0.8%)

Remove: (sort a1 a2)
Compiler: Compiled 327 to 187 computations (42.8% saved)