Details

analyze539.0ms (3.2%)

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)

sample5.1s (30.7%)

Results

1.8s	5431×	body	256	valid
1.1s	1891×	body	1024	valid
967.0ms	1565×	body	1024	invalid
496.0ms	1567×	body	256	invalid
347.0ms	931×	body	512	valid
298.0ms	828×	body	512	invalid
4.0ms	3×	body	2048	valid

preprocess28.0ms (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 (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs

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

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

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

eval2.0ms (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

0.5b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 37 to 25 computations (32.4% saved)

localize42.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 37 to 16 computations (56.8% saved)

series14.0ms (0.1%)

Counts

2 → 40

Calls

12 calls:

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

rewrite64.0ms (0.4%)

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

Outputs
((#(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))))))
((#(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))))))))

Outputs

((#(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))))))

((#(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))))))))

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

821×	`unswap-sqr_binary64`
749×	`associate-l_binary64`
547×	`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	1196	821
4	4370	806

Stop Event

1×	node limit

Counts

126 → 109

Calls

Call 1

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

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

localize55.0ms (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)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series15.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite156.0ms (0.9%)

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	3917	45

Stop Event

1×	node limit

Counts

3 → 147

Calls

Call 1

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

Inputs

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

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

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

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

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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))))))) (#(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 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(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 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))))))) (#(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 a1 a1) (/.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)) a2) 1) a2 (/.f64 (*.f64 a1 a1) (/.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)) a2) (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 a2) (/.f64 (*.f64 a1 a1) (/.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)) a2) (sqrt.f64 a2)) (sqrt.f64 a2) (/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))))))))

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

751×	`associate-+l+_binary64`
730×	`associate-/l*_binary64`
509×	`associate-+r+_binary64`
509×	`associate-/r*_binary64`
442×	`*-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 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (*.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 (+.f64 (.f64 1/24 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 1/24 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 4)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(+.f64 (.f64 (+.f64 (.f64 -1/2 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 2)) (+.f64 (.f64 (+.f64 (.f64 -1/720 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 6)) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 (+.f64 (.f64 1/24 (/.f64 (pow.f64 a2 2) (sqrt.f64 2))) (*.f64 1/24 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))) (pow.f64 th 4)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))

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

eval231.0ms (1.4%)

Compiler: Compiled 9104 to 5245 computations (42.4% saved)

prune148.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	382	13	395
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	383	14	397

Error

Counts

397 → 14

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	30.7b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
	0.5b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	30.7b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	24.3b	(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (.f64 a1 (/.f64 a1 (sqrt.f64 2))))
	43.2b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 6))
▶	24.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	24.7b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
▶	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	24.3b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
▶	0.5b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	0.4b	(fma.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (pow.f64 2 -1/2) (/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th))))

Compiler

Compiled 403 to 304 computations (24.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 35 to 19 computations (45.7% saved)

series31.0ms (0.2%)

Counts

4 → 88

Calls

24 calls:

Time	Variable		Point	Expression
9.0ms	a2	@	0	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
5.0ms	a1	@	0	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
4.0ms	a1	@	inf	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
1.0ms	a2	@	inf	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
1.0ms	a1	@	-inf	(pow.f64 (hypot.f64 a2 a1) 2)

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`log-prod_binary64`
451×	`exp-prod_binary64`
292×	`pow2_binary64`
289×	`pow-prod-down_binary64`
204×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	235	36
2	2972	36

Stop Event

1×	node limit

Counts

4 → 181

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 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 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a2 a1) (.f64 (hypot.f64 a2 a1) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) (.f64 2 (pow.f64 (cos.f64 th) -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) (.f64 2 (pow.f64 (cos.f64 th) -2)))) (cbrt.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 4) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) 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(cos.f64 th) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 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 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (hypot.f64 a2 a1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 6) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))))) (#(struct:change 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((#(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) 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-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 (cos.f64 th) (sqrt.f64 2)) -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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 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 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 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 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(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 (hypot.f64 a2 a1) (hypot.f64 a2 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 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 4) (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2) (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a2 a1)) (pow.f64 (hypot.f64 a2 a1) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a2 a1) 3/2) (sqrt.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 5) (cbrt.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))))) (#(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 sqrt.f64 (pow.f64 (hypot.f64 a2 a1) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 6))))) (#(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 exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 a2 a1) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (cbrt.f64 (hypot.f64 a2 a1)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 a2 a1)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a2 a1))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a2 a2 (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 a1 a1 (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (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 (.f64 (cbrt.f64 a2) a2) (pow.f64 (cbrt.f64 a2) 2) (.f64 a1 a1))))) (#(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 a1) a1) (pow.f64 (cbrt.f64 a1) 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 (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))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (hypot.f64 a2 a1))) 2)) (log.f64 (cbrt.f64 (exp.f64 (hypot.f64 a2 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a2 a1)))) (log.f64 (sqrt.f64 (exp.f64 (hypot.f64 a2 a1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (hypot.f64 a2 a1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 a2 a1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (hypot.f64 a2 a1)) (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2) (cbrt.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 4)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 a2 a1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a2 a1) 6) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 a2 a1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 a2 a1)) 2) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 a2 a1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (hypot.f64 a2 a1))) 2)) (cbrt.f64 (log.f64 (hypot.f64 a2 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (hypot.f64 a2 a1)))) (sqrt.f64 (log.f64 (hypot.f64 a2 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a2 a1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (hypot.f64 a2 a1))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (hypot.f64 a2 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 a2 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 a2 a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a2 a1))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (hypot.f64 a2 a1))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (hypot.f64 a2 a1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (hypot.f64 a2 a1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 a2 a1)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a2 a1))) 1) 1/2))))))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

796×	`times-frac_binary64`
631×	`associate-/l*_binary64`
562×	`associate-/r*_binary64`
409×	`distribute-rgt-in_binary64`
394×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	280	2949
1	850	2759
2	2914	2439

Stop Event

1×	node limit

Counts

269 → 265

Calls

Call 1

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

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

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series11.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	th	@	0	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
1.0ms	a2	@	inf	(/.f64 a2 (sqrt.f64 2))
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	a2	@	0	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))

rewrite75.0ms (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 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(.f64 a2 (.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 (*.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))))))))

((#(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)))))))))

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	53	764
1	135	760
2	350	758
3	1144	732
4	3627	698
5	5293	678
6	5469	678
7	5679	678
8	5894	678
9	6098	678

Stop Event

1×	node limit

Counts

117 → 89

Calls

Call 1

Inputs
(/.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))
(/.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))

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

localize23.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
✓	0.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series7.0ms (0%)

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	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	th	@	-inf	(.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)))

rewrite82.0ms (0.5%)

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

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

simplify56.0ms (0.3%)

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

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

series4.0ms (0%)

Counts

2 → 20

Calls

12 calls:

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

rewrite69.0ms (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 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (pow.f64 a2 2) (cos.f64 th))

Outputs

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

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

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

952×	`fma-def_binary64`
617×	`associate-*l/_binary64`
520×	`distribute-rgt-out_binary64`
494×	`*-commutative_binary64`
488×	`associate-/l*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	43	358
1	111	339
2	327	326
3	1336	299
4	4865	280
5	6771	266
6	7997	266

Stop Event

1×	node limit

Counts

74 → 72

Calls

Call 1

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

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

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 2)
✓	0.1b	(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))
✓	0.2b	(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
✓	0.3b	(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))

Compiler

Compiled 57 to 33 computations (42.1% saved)

series93.0ms (0.6%)

Counts

4 → 132

Calls

33 calls:

Time	Variable		Point	Expression
45.0ms	th	@	inf	(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))
17.0ms	th	@	inf	(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
4.0ms	a2	@	0	(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
3.0ms	a1	@	0	(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))
3.0ms	a2	@	0	(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))

rewrite85.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

671×	`log-prod_binary64`
340×	`pow2_binary64`
238×	`pow1/3_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	281	54
2	3524	54

Stop Event

1×	node limit

Counts

4 → 159

Calls

Call 1

Inputs
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(*.f64 (cos.f64 th) (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 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))))) (#(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) (pow.f64 2 -1/4)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))))))) (#(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) (pow.f64 2 -1/4))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (cos.f64 th)) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (/.f64 1 (.f64 (pow.f64 4 1/8) (pow.f64 (hypot.f64 a1 a2) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (pow.f64 2 -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/12)) (cbrt.f64 (/.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4) (sqrt.f64 2))) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4)) (.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/16)) (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 2 -1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 th) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (/.f64 1 (neg.f64 (pow.f64 4 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/4) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) 1) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1) (/.f64 (cos.f64 th) (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (pow.f64 4 1/8)) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4)) 1) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 1) (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 2 1/12) -2) (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4)) (cbrt.f64 (sqrt.f64 2))) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2))) (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 2 1/12)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cos.f64 th) (pow.f64 4 1/16)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 4 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 4 1/16)) (/.f64 (cos.f64 th) (pow.f64 4 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 -1/8) (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 4 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4)) (pow.f64 4 1/16)) (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 4 1/16)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 th) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4) (sqrt.f64 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/16)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/12)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/16)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (pow.f64 4 1/8) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 6) (pow.f64 2 3/4)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (/.f64 (pow.f64 4 1/8) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (pow.f64 4 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) 4) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/4))))))) (#(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) (pow.f64 2 -1/4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (sqrt.f64 (cos.f64 th))) (pow.f64 4 1/16)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 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simplify152.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

650×	`times-frac_binary64`
545×	`fma-def_binary64`
493×	`associate-/l*_binary64`
419×	`associate-/r*_binary64`
359×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	5235
1	1054	4482
2	4067	3762

Stop Event

1×	node limit

Counts

291 → 261

Calls

Call 1

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

eval901.0ms (5.4%)

Compiler: Compiled 20691 to 13598 computations (34.3% saved)

prune316.0ms (1.9%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	881	19	900
Fresh	7	1	8
Picked	1	0	1
Done	3	2	5
Total	892	22	914

Error

Counts

914 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	30.7b	(.f64 (pow.f64 1/4 1/4) (.f64 (pow.f64 a1 2) (cos.f64 th)))
	24.3b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 1/4 1/4))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	24.7b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
	30.7b	(/.f64 (/.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
	30.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	24.7b	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
▶	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	24.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	30.7b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
✓	24.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
▶	24.7b	(.f64 (pow.f64 2 -1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	24.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	33.2b	(/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	30.7b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	0.5b	(.f64 (.f64 (neg.f64 (cos.f64 th)) (/.f64 1 (neg.f64 (sqrt.f64 2)))) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
▶	39.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	30.7b	(.f64 (cos.f64 th) (.f64 a1 (*.f64 a1 (pow.f64 1/4 1/4))))
	42.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	39.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	24.7b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))

Compiler

Compiled 588 to 440 computations (25.2% saved)

localize20.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 41 to 20 computations (51.2% saved)

series7.0ms (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)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms	th	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms	th	@	-inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms	a1	@	0	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
1.0ms	th	@	0	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
408×	`exp-prod_binary64`
373×	`pow-prod-down_binary64`
299×	`pow2_binary64`
208×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	244	25
2	2791	25

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify87.0ms (0.5%)

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	1876	810
4	5154	806

Stop Event

1×	node limit

Counts

100 → 75

Calls

Call 1

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

localize21.0ms (0.1%)

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)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite61.0ms (0.4%)

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)))))))))

simplify105.0ms (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)))

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
✓	0.3b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))
✓	0.5b	(/.f64 (sqrt.f64 2) a2)

Compiler

Compiled 30 to 19 computations (36.7% saved)

series6.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite69.0ms (0.4%)

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

Outputs

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

simplify119.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	51	764
1	132	760
2	348	758
3	1138	732
4	3627	698
5	5293	678
6	5469	678
7	5680	678
8	5895	678
9	6099	678

Stop Event

1×	node limit

Counts

200 → 171

Calls

Call 1

Inputs
(/.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 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 (*.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 (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))

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 15 computations (46.4% saved)

series4.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	a2	@	-inf	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
0.0ms	a2	@	0	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
0.0ms	th	@	0	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
0.0ms	th	@	-inf	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))
0.0ms	a2	@	0	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))

rewrite70.0ms (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 a2 a2) (sqrt.f64 2))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th))

Outputs

((#(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)))))))

((#(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))))))))

simplify103.0ms (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	871	514
4	2819	495
5	4560	483
6	6019	483
7	6321	483
8	6549	483
9	6756	483

Stop Event

1×	node limit

Counts

94 → 69

Calls

Call 1

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

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

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 32 to 15 computations (53.1% saved)

series8.0ms (0.1%)

Counts

3 → 64

Calls

18 calls:

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

rewrite61.0ms (0.4%)

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 a2 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(*.f64 a2 (cos.f64 th))

Outputs

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

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

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

simplify194.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

750×	`*-commutative_binary64`
697×	`sqr-pow_binary64`
460×	`fma-def_binary64`
434×	`distribute-rgt-out_binary64`
368×	`pow-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	840
1	165	825
2	481	772
3	1968	747
4	3726	747
5	3984	747
6	4213	747
7	4448	747
8	4783	747
9	5388	747
10	5952	747
11	6251	747
12	6592	747
13	7002	747
14	7485	747

Stop Event

1×	node limit

Counts

103 → 70

Calls

Call 1

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

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

eval135.0ms (0.8%)

Compiler: Compiled 6277 to 4008 computations (36.1% saved)

prune106.0ms (0.6%)

Pruning

28 alts after pruning (24 fresh and 4 done)

	Pruned	Kept	Total
New	423	15	438
Fresh	6	9	15
Picked	1	0	1
Done	2	4	6
Total	432	28	460

Error

Counts

460 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	30.7b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
	30.7b	(.f64 (cos.f64 th) (.f64 a1 (*.f64 a1 (pow.f64 1/4 1/4))))
	42.7b	(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (.f64 -1/2 (*.f64 th th))))
	39.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	39.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
✓	24.7b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
	43.2b	(-.f64 (+.f64 1 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1)
	30.7b	(/.f64 (/.f64 (.f64 (.f64 a1 a1) (cos.f64 th)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
▶	30.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	39.2b	(.f64 a2 (.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
▶	0.5b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	39.2b	(.f64 a2 (.f64 (pow.f64 2 -1/2) a2))
	30.7b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
✓	24.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	24.3b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
	30.7b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	39.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
✓	39.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	43.2b	(*.f64 a2 (-.f64 (+.f64 1 (/.f64 a2 (sqrt.f64 2))) 1))
	39.4b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	42.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	24.7b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
▶	39.2b	(*.f64 a2 (pow.f64 (/.f64 (sqrt.f64 2) a2) -1))
	39.3b	(.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2)))
	24.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	24.7b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))

Compiler

Compiled 657 to 502 computations (23.6% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 1/2) (cos.f64 th))
✓	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))

Compiler

Compiled 37 to 16 computations (56.8% saved)

series4.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

987×	`pow1_binary64`
905×	`add-log-exp_binary64`
905×	`log1p-expm1-u_binary64`
905×	`expm1-log1p-u_binary64`
108×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	218	25
2	2513	25

Stop Event

1×	node limit

Counts

2 → 30

Calls

Call 1

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

Outputs

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

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

839×	`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	52	894
1	146	820
2	436	774
3	1894	746
4	5245	742

Stop Event

1×	node limit

Counts

70 → 52

Calls

Call 1

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

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

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	a2	@	0	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
1.0ms	a2	@	inf	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
0.0ms	a2	@	-inf	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))

rewrite41.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

501×	`pow1_binary64`
481×	`add-sqr-sqrt_binary64`
464×	`add-log-exp_binary64`
464×	`log1p-expm1-u_binary64`
464×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	121	9
2	1340	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify170.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
441×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	108
1	13	108
2	23	108
3	44	108
4	107	108
5	328	108
6	1230	108
7	2107	108
8	2271	108
9	2455	108
10	2663	108
11	2959	108
12	3352	108
13	3833	108
14	4401	108
15	5091	108
16	5926	108
17	6320	108
18	6610	108
19	6884	108
20	6954	108
21	6988	108
22	7929	108

Stop Event

1×	node limit

Counts

23 → 13

Calls

Call 1

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

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

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a2 (.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
✓	0.5b	(*.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))
✓	1.0b	(/.f64 1 (neg.f64 (sqrt.f64 2)))

Compiler

Compiled 36 to 29 computations (19.4% saved)

series2.0ms (0%)

Counts

3 → 24

Calls

6 calls:

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

rewrite111.0ms (0.7%)

Algorithm

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

Rules

98×	`add-sqr-sqrt_binary64`
98×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
93×	`pow1_binary64`
93×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	208	28
2	2942	28
0	6	8
1	121	8
2	1447	8
0	6	8
0	9	10
1	186	10
2	2505	10
0	9	10
0	10	13
1	208	13
2	2942	13
0	10	13

Stop Event

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

Counts

3 → 25

Calls

Call 1

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

Outputs

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

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

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

simplify108.0ms (0.6%)

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	7	180
1	12	180
2	21	180
3	38	180
4	86	180
5	274	180
6	1103	180
7	3496	180
8	4318	180
9	4503	180
10	4719	180
11	5069	180
12	5499	180
13	5982	180
14	6634	180
15	7323	180

Stop Event

1×	node limit

Counts

49 → 28

Calls

Call 1

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

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 a2 (pow.f64 (/.f64 (sqrt.f64 2) a2) -1))
✓	0.3b	(pow.f64 (/.f64 (sqrt.f64 2) a2) -1)
	0.5b	(/.f64 (sqrt.f64 2) a2)

Compiler

Compiled 26 to 21 computations (19.2% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`pow1_binary64`
707×	`add-log-exp_binary64`
707×	`log1p-expm1-u_binary64`
707×	`expm1-log1p-u_binary64`
691×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	167	15
2	1973	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

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

simplify108.0ms (0.6%)

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	7	180
1	12	180
2	21	180
3	38	180
4	86	180
5	274	180
6	1103	180
7	3496	180
8	4318	180
9	4503	180
10	4719	180
11	5069	180
12	5499	180
13	5982	180
14	6634	180
15	7323	180

Stop Event

1×	node limit

Counts

78 → 56

Calls

Call 1

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 15 computations (44.4% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite57.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

497×	`log-prod_binary64`
394×	`exp-prod_binary64`
340×	`prod-exp_binary64`
269×	`pow-prod-down_binary64`
245×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	193	14
2	2603	14

Stop Event

1×	node limit

Counts

1 → 71

Calls

Call 1

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

Outputs

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

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1132×	`unswap-sqr_binary64`
659×	`associate-*l/_binary64`
607×	`fma-def_binary64`
494×	`associate-*r/_binary64`
372×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	32	424
1	83	424
2	230	424
3	857	406
4	2734	387
5	4348	375
6	5665	375
7	5970	375
8	6198	375
9	6407	375

Stop Event

1×	node limit

Counts

95 → 81

Calls

Call 1

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

eval108.0ms (0.6%)

Compiler: Compiled 4637 to 3163 computations (31.8% saved)

prune69.0ms (0.4%)

Pruning

32 alts after pruning (25 fresh and 7 done)

	Pruned	Kept	Total
New	323	13	336
Fresh	7	12	19
Picked	0	1	1
Done	2	6	8
Total	332	32	364

Error

Counts

364 → 32

Alt Table

Click to see full alt table

Status	Error	Program
	30.7b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
	43.7b	(/.f64 (.f64 (+.f64 1 (.f64 th (*.f64 th -1/2))) a1) (/.f64 (sqrt.f64 2) a1))
	30.7b	(.f64 (cos.f64 th) (.f64 a1 (*.f64 a1 (pow.f64 1/4 1/4))))
	42.7b	(.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (+.f64 1 (.f64 -1/2 (*.f64 th th))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	39.2b	(.f64 a2 (.f64 (/.f64 1 (sqrt.f64 2)) a2))
✓	39.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
✓	24.7b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
	39.8b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	42.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	24.7b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	24.3b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
	24.7b	(.f64 (.f64 a2 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) a2))
✓	0.5b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	39.2b	(pow.f64 (*.f64 a2 (pow.f64 1/2 1/4)) 2)
✓	24.7b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	30.7b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
	39.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	39.8b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	39.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	39.2b	(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
✓	39.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	43.2b	(*.f64 a2 (-.f64 (+.f64 1 (/.f64 a2 (sqrt.f64 2))) 1))
	39.4b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
✓	30.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	30.7b	(.f64 a1 (.f64 (cos.f64 th) (*.f64 (sqrt.f64 1/2) a1)))
	39.2b	(*.f64 a2 (/.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 1 a2)))
	39.3b	(.f64 a2 (sqrt.f64 (/.f64 (.f64 a2 a2) 2)))
	24.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	24.7b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
	43.2b	(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)

Compiler

Compiled 394 to 301 computations (23.6% saved)

regimes346.0ms (2.1%)

Counts

62 → 1

Calls

Call 1

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

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

Calls

11 calls:

38.0ms	a1
37.0ms	th
37.0ms	a2
34.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
31.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

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

Compiler

Compiled 718 to 422 computations (41.2% saved)

regimes241.0ms (1.4%)

Counts

55 → 1

Calls

Call 1

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

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

Calls

8 calls:

38.0ms	a1
32.0ms	th
32.0ms	a2
27.0ms	(cos.f64 th)
24.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

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

Compiler

Compiled 571 to 333 computations (41.7% saved)

regimes195.0ms (1.2%)

Counts

52 → 1

Calls

Call 1

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

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

Calls

7 calls:

32.0ms	th
32.0ms	a2
32.0ms	a1
24.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
24.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 526 to 311 computations (40.9% saved)

regimes576.0ms (3.5%)

Counts

45 → 4

Calls

Call 1

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

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

Calls

9 calls:

115.0ms	a1
115.0ms	th
73.0ms	a2
55.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
51.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.7b	5	`th`
9.4b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.4b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.4b	3	`(cos.f64 th)`
8.6b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 456 to 281 computations (38.4% saved)

bsearch179.0ms (1.1%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
58.0ms	-3.2040251015145385e-132	-1.0682734652474209e-144
59.0ms	-6.052530258782011e-112	-5.101457747724082e-115
61.0ms	-3.7205729887072595e-21	-6.006095108509966e-24

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes508.0ms (3%)

Counts

40 → 4

Calls

Call 1

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

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

Calls

9 calls:

109.0ms	th
108.0ms	a1
66.0ms	a2
43.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
42.0ms	(cos.f64 th)

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.8b	5	`th`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(cos.f64 th)`
8.6b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 404 to 256 computations (36.6% saved)

bsearch269.0ms (1.6%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
67.0ms	-3.2040251015145385e-132	-1.0682734652474209e-144
106.0ms	-6.052530258782011e-112	-5.101457747724082e-115
95.0ms	-6.006095108509966e-24	-1.8160145739559853e-29

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes582.0ms (3.5%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

9 calls:

190.0ms	a1
102.0ms	th
62.0ms	a2
42.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
42.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.8b	5	`th`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(cos.f64 th)`
8.6b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 395 to 251 computations (36.5% saved)

bsearch104.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
104.0ms	2.8786861742659004e-140	1.1374409519676902e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes490.0ms (2.9%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

8 calls:

95.0ms	a1
93.0ms	th
59.0ms	a2
52.0ms	(*.f64 a2 a2)
46.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.8b	5	`th`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.5b	3	`(cos.f64 th)`
8.6b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 371 to 238 computations (35.8% saved)

bsearch59.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
58.0ms	2.8786861742659004e-140	1.1374409519676902e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes327.0ms (2%)

Counts

33 → 2

Calls

Call 1

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

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

Calls

7 calls:

83.0ms	a1
81.0ms	th
48.0ms	a2
36.0ms	(cos.f64 th)
29.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.8b	5	`th`
9.5b	3	`(cos.f64 th)`
8.6b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 325 to 211 computations (35.1% saved)

bsearch58.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
57.0ms	2.8786861742659004e-140	1.1374409519676902e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes279.0ms (1.7%)

Counts

27 → 2

Calls

Call 1

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

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

Calls

7 calls:

72.0ms	th
63.0ms	a1
40.0ms	a2
32.0ms	(cos.f64 th)
26.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
6.6b	4	`a1`
6.6b	2	`a2`
9.8b	5	`th`
9.5b	3	`(cos.f64 th)`
8.7b	4	`(*.f64 a1 a1)`
10.2b	2	`(*.f64 a2 a2)`
10.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 271 to 185 computations (31.7% saved)

bsearch64.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
64.0ms	2.8786861742659004e-140	1.1374409519676902e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes208.0ms (1.2%)

Counts

26 → 2

Calls

Call 1

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

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

Calls

7 calls:

43.0ms	a2
40.0ms	th
27.0ms	a1
26.0ms	(*.f64 a2 a2)
24.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
13.4b	2	`a1`
13.0b	2	`a2`
11.1b	3	`th`
11.0b	2	`(cos.f64 th)`
14.1b	2	`(*.f64 a1 a1)`
15.1b	2	`(*.f64 a2 a2)`
15.1b	2	`(*.f64 a2 a2)`

Compiler

Compiled 262 to 181 computations (30.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9816955326641235	0.9929678545344341

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes83.0ms (0.5%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

6 calls:

16.0ms	a2
16.0ms	a1
15.0ms	th
9.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
24.3b	1	`a1`
24.3b	1	`a2`
24.3b	1	`th`
24.3b	1	`(*.f64 a1 a1)`
24.3b	1	`(*.f64 a2 a2)`
24.3b	1	`(*.f64 a2 a2)`

Compiler

Compiled 248 to 171 computations (31% saved)

regimes69.0ms (0.4%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

5 calls:

14.0ms	a1
14.0ms	a2
14.0ms	th
9.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
24.4b	1	`a1`
24.4b	1	`a2`
24.4b	1	`th`
24.4b	1	`(*.f64 a1 a1)`
24.4b	1	`(*.f64 a2 a2)`

Compiler

Compiled 233 to 163 computations (30% saved)

regimes121.0ms (0.7%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

6 calls:

35.0ms	th
20.0ms	a1
19.0ms	a2
15.0ms	(*.f64 a1 a1)
14.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.3b	2	`a1`
26.7b	2	`a2`
35.8b	4	`th`
29.2b	2	`(*.f64 a1 a1)`
29.2b	2	`(*.f64 a1 a1)`
28.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 170 to 119 computations (30% saved)

bsearch61.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
60.0ms	3.162261452390262e-78	3.689156631956354e-72

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes93.0ms (0.6%)

Counts

12 → 2

Calls

Call 1

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

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

Calls

6 calls:

26.0ms	th
16.0ms	a2
14.0ms	a1
11.0ms	(*.f64 a1 a1)
11.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
27.3b	2	`a1`
26.7b	2	`a2`
35.8b	4	`th`
29.2b	2	`(*.f64 a1 a1)`
29.2b	2	`(*.f64 a1 a1)`
28.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 112 to 76 computations (32.1% saved)

bsearch60.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	3.162261452390262e-78	3.689156631956354e-72

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes69.0ms (0.4%)

Counts

5 → 2

Calls

Call 1

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

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

Calls

7 calls:

16.0ms	th
9.0ms	a1
9.0ms	a2
8.0ms	(*.f64 a1 a1)
8.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
27.3b	2	`a1`
26.7b	2	`a2`
35.8b	4	`th`
29.3b	2	`(*.f64 a1 a1)`
29.3b	2	`(*.f64 a1 a1)`
28.2b	2	`(*.f64 a2 a2)`
28.2b	2	`(*.f64 a2 a2)`

Compiler

Compiled 69 to 48 computations (30.4% saved)

bsearch61.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
61.0ms	3.162261452390262e-78	3.689156631956354e-72

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes27.0ms (0.2%)

Accuracy

Total -27.9b remaining (-104.3%)

Threshold costs -27.9b (-104.3%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

13.0ms	th
6.0ms	a1
6.0ms	a2

Results

Error	Segments	Branch
27.4b	2	`a1`
26.7b	2	`a2`
35.8b	4	`th`

Compiler

Compiled 27 to 20 computations (25.9% saved)

bsearch59.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	3.162261452390262e-78	3.689156631956354e-72

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	511
1	98	511

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a1 -4945489776950845/1329227995784915872903807060280344576) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))
(if (<=.f64 a1 -1021884129738021/170141183460469231731687303715884105728) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (/.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (.f64 (.f64 a2 (cos.f64 th)) (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (.f64 a2 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 (cos.f64 th) 4458563631096791/4503599627370496) (.f64 (.f64 a2 (cos.f64 th)) (.f64 (sqrt.f64 1/2) a2)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 a2 (sqrt.f64 (/.f64 (*.f64 a2 a2) 2))))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

Outputs
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a1 -4945489776950845/1329227995784915872903807060280344576) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))
(if (<=.f64 a1 -4945489776950845/1329227995784915872903807060280344576) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2)))))))
(if (<=.f64 a1 -1021884129738021/170141183460469231731687303715884105728) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))))))
(if (<=.f64 a1 -1021884129738021/170141183460469231731687303715884105728) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -6555338758310193/10830740992659433045228180406808920716548582325686783496759685861775864483615725089999900023844295226942934417817982702456930304) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 1/2)) (if (<=.f64 a1 -5121106286504479/1598335257761788022467377781654101148543282249044465229239888363328190330275719997501596724768507889233831388734160190922469363547795602076820570112) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 2)))))))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (/.f64 (.f64 (*.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 a1 (sqrt.f64 1/2)))) (/.f64 (.f64 a2 (*.f64 a2 (cos.f64 th))) (sqrt.f64 2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 a1 (sqrt.f64 1/2)))) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) a1))) (.f64 (.f64 a2 (cos.f64 th)) (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 a1 (.f64 (cos.f64 th) (.f64 a1 (sqrt.f64 1/2)))) (.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (.f64 a2 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a2 6175499410422153/214524926879081553593184399971293538039669853129478294043576983099548224481176751628829988770670454843040509730983776813660062124991145119142938384097345536) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 (.f64 a2 (cos.f64 th)) (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 (cos.f64 th) 4458563631096791/4503599627370496) (.f64 (.f64 a2 (cos.f64 th)) (.f64 (sqrt.f64 1/2) a2)) (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (*.f64 a1 a1))))
(if (<=.f64 (cos.f64 th) 4458563631096791/4503599627370496) (.f64 (.f64 a2 (cos.f64 th)) (.f64 a2 (sqrt.f64 1/2))) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 1/2))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (/.f64 1 (sqrt.f64 2)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 a2 (sqrt.f64 (/.f64 (*.f64 a2 a2) 2))))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a2 1649059928344245/521481209941628438084722096232800809229175908778479680162851955034721612739414196782949728256) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

Compiler

Compiled 387 to 262 computations (32.3% saved)

soundness0.0ms (0%)

end167.0ms (1%)

Remove: (sort a1 a2)
Compiler: Compiled 367 to 206 computations (43.9% saved)