Details

analyze491.0ms (2.9%)

Algorithm

1×

Search

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

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample5.0s (29.2%)

Results

1.3s	1864×	body	1024	valid
1.3s	5477×	body	256	valid
1.1s	1620×	body	1024	invalid
432.0ms	1511×	body	256	invalid
409.0ms	796×	body	512	invalid
377.0ms	914×	body	512	valid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	2048	valid

preprocess29.0ms (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)))

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.5b

Counts

3 → 1

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)))

Compiler

Compiled 15 to 10 computations (33.3% saved)

localize15.0ms (0.1%)

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	@	0	(.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)))

rewrite63.0ms (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)))

eval37.0ms (0.2%)

Compiler: Compiled 1964 to 1149 computations (41.5% saved)

prune31.0ms (0.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	96	13	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	96	14	110

Error

0.0b

Counts

110 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	19.2b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	0.4b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
▶	30.5b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
✓	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) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))
▶	25.2b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.2b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
▶	36.5b	(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
	1.0b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))
▶	0.4b	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	0.9b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	29.4b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	30.5b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))

Compiler

Compiled 393 to 304 computations (22.6% saved)

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.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	@	0	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms	th	@	inf	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
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)))

rewrite60.0ms (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))))))

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))))))

simplify57.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	53	958
1	148	884
2	437	838
3	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))

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series15.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
4.0ms	th	@	-inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
2.0ms	a2	@	0	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
1.0ms	th	@	inf	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
1.0ms	th	@	inf	(*.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
1.0ms	th	@	-inf	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 69

Calls

Call 1

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

Outputs

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

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

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

simplify118.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

117 → 89

Calls

Call 1

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

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

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 18 computations (35.7% saved)

series7.0ms (0%)

Counts

2 → 8

Calls

12 calls:

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

rewrite57.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify52.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

62 → 70

Calls

Call 1

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

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

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 35 to 19 computations (45.7% saved)

series25.0ms (0.1%)

Counts

4 → 88

Calls

24 calls:

Time	Variable		Point	Expression
5.0ms	a1	@	0	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
5.0ms	a2	@	0	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
2.0ms	th	@	0	(/.f64 (sqrt.f64 2) (cos.f64 th))
2.0ms	a2	@	inf	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
1.0ms	a1	@	inf	(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite78.0ms (0.5%)

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

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

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

796×	`times-frac_binary64`
631×	`associate-/l*_binary64`
567×	`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	2915	2439

Stop Event

1×	node limit

Counts

269 → 265

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (cos.f64 th))) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 12) (.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a2 8))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 2)))) (pow.f64 a2 2))) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4)))))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6)))) (pow.f64 a2 4))) (.f64 1/256 (/.f64 1 (pow.f64 a2 10)))))) (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (.f64 1/16 (/.f64 1 (pow.f64 a2 6))))) (.f64 5/64 (/.f64 1 (pow.f64 a2 6)))) (*.f64 (pow.f64 a1 8) (cos.f64 th))) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2)))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 2))) (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a1 4))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (.f64 (cos.f64 th) (pow.f64 a2 8))) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (.f64 (pow.f64 a2 8) (cos.f64 th))) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a1 8))) (.f64 -1/2 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 2)))) (pow.f64 a1 2))) (+.f64 (.f64 1/8 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4))) (+.f64 (.f64 1/256 (/.f64 1 (pow.f64 a1 10))) (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (-.f64 (.f64 1/64 (/.f64 1 (pow.f64 a1 8))) (.f64 -1/2 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 2)))) (pow.f64 a1 2))) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a1 5)) 2) (.f64 1/8 (/.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (pow.f64 a1 4))))))))) (.f64 (cos.f64 th) (pow.f64 a2 12))) (sqrt.f64 2)) (/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2)))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 1/8 (pow.f64 a1 6)) (.f64 -1/8 (pow.f64 a1 6))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 4))) (+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))) (cos.f64 th)) (.f64 (sqrt.f64 2) (pow.f64 a2 2))))))
(/.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))))))
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)))))
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))))
(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) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (/.f64 a2 (/.f64 (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 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th)) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a2 (sqrt.f64 2)) a2) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1)))
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(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (*.f64 th th))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (sqrt.f64 2))
(fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) -5/24)))))
(-.f64 (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (sqrt.f64 2)) (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) -5/24)))
(+.f64 (sqrt.f64 2) (.f64 (sqrt.f64 2) (-.f64 (.f64 (.f64 th th) 1/2) (.f64 -5/24 (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (sqrt.f64 2) (fma.f64 -1 (.f64 (pow.f64 th 6) (fma.f64 -1/720 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) -5/24) (.f64 (sqrt.f64 2) 1/48)))) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (*.f64 (sqrt.f64 2) -5/24))))))
(+.f64 (sqrt.f64 2) (-.f64 (-.f64 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) 1/2)) (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) -5/24))) (.f64 (pow.f64 th 6) (fma.f64 (sqrt.f64 2) -1/720 (fma.f64 (sqrt.f64 2) 1/48 (*.f64 (sqrt.f64 2) -5/48))))))
(+.f64 (.f64 (sqrt.f64 2) (-.f64 (.f64 (.f64 th th) 1/2) (.f64 -5/24 (pow.f64 th 4)))) (-.f64 (sqrt.f64 2) (.f64 (pow.f64 th 6) (fma.f64 (sqrt.f64 2) -1/720 (.f64 (sqrt.f64 2) -1/12)))))
a2
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 a1 2) a2)) a2)
(fma.f64 1/2 (/.f64 (*.f64 a1 a1) a2) a2)
(fma.f64 1/2 (/.f64 a1 (/.f64 a2 a1)) a2)
(fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)
(+.f64 (.f64 -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))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.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)))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (*.f64 (/.f64 a1 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 a2) a1) 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 a2 (/.f64 a1 a2)))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) a1) (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.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 a2 (/.f64 a1 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 1/2 (/.f64 (.f64 a2 a2) a1))) (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 a2 (/.f64 a1 a2))) a1)
(-.f64 (.f64 -1/2 (/.f64 (.f64 a2 a2) a1)) 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 a2) a1) (.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 a2) a1) (.f64 1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))) a1)
a1
(+.f64 a1 (*.f64 1/2 (/.f64 (pow.f64 a2 2) a1)))
(+.f64 a1 (.f64 1/2 (/.f64 (.f64 a2 a2) a1)))
(fma.f64 1/2 (/.f64 a2 (/.f64 a1 a2)) a1)
(fma.f64 1/2 (/.f64 (*.f64 a2 a2) a1) 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 a2 (/.f64 a1 a2)))))
(+.f64 (fma.f64 1/2 (/.f64 (.f64 a2 a2) a1) a1) (.f64 -1/8 (/.f64 (pow.f64 a2 4) (pow.f64 a1 3))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 a2 6) (pow.f64 a1 5))) (+.f64 a1 (+.f64 (.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 a2 (/.f64 a1 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 1/2 (/.f64 (.f64 a2 a2) a1))) (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)
(fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2)
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.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))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (*.f64 (/.f64 a1 a2) a1) a2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3))) (+.f64 (.f64 1/2 (/.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)))
(fma.f64 -1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (fma.f64 1/2 (*.f64 (/.f64 a1 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))
(-.f64 (*.f64 -1/2 (/.f64 a1 (/.f64 a2 a1))) a2)
(-.f64 (.f64 (/.f64 -1/2 a2) (.f64 a1 a1)) 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 (fma.f64 -1/2 (.f64 (/.f64 a1 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 (/.f64 (pow.f64 a1 6) (pow.f64 a2 5)) -1/16)) a2))
(fma.f64 -1/2 (.f64 (/.f64 a1 a2) a1) (-.f64 (fma.f64 1/8 (/.f64 (pow.f64 a1 4) (pow.f64 a2 3)) (.f64 (/.f64 -1/16 (pow.f64 a2 5)) (pow.f64 a1 6))) a2))
(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 (.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)))
(fma.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))) (pow.f64 a1 8) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(fma.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)))) (pow.f64 a1 8) (fma.f64 a2 a2 (*.f64 a1 a1)))
(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)))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (/.f64 (pow.f64 a2 4) a1) (/.f64 1/4 a1)))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (*.f64 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 (/.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 6)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (pow.f64 a1 2))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 (/.f64 (pow.f64 a2 4) a1) (/.f64 1/4 a1)))))
(fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 a1 a1 (.f64 1/4 (/.f64 (pow.f64 a2 4) (*.f64 a1 a1))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a2 2) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 4) (pow.f64 a1 2))) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4))))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (+.f64 (.f64 a2 a2) (+.f64 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (.f64 a1 a1)) (*.f64 1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)))))))
(fma.f64 -1/8 (/.f64 (pow.f64 a2 6) (pow.f64 a1 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a2 a2 (fma.f64 1/4 (/.f64 (pow.f64 a2 4) (.f64 a1 a1)) (fma.f64 a1 a1 (*.f64 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 (/.f64 1/8 (pow.f64 a1 4)) (pow.f64 a2 6)))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 (+.f64 (.f64 -1 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 a1 6))) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (.f64 5/64 (/.f64 1 (pow.f64 a1 6)))) (pow.f64 a2 8)) (pow.f64 a1 2)))
(+.f64 (.f64 a2 a2) (fma.f64 (fma.f64 -1 (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (/.f64 5/64 (pow.f64 a1 6))) (pow.f64 a2 8) (.f64 a1 a1)))
(fma.f64 a2 a2 (fma.f64 a1 a1 (*.f64 (pow.f64 a2 8) (-.f64 (/.f64 5/64 (pow.f64 a1 6)) (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))))))
(fma.f64 a2 a2 (fma.f64 (pow.f64 a2 8) (-.f64 (.f64 (/.f64 1 (pow.f64 a1 6)) 1/64) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2)) (.f64 a1 a1)))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (+.f64 (.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 a2 4) (pow.f64 a1 6))))))))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (/.f64 (pow.f64 a1 4) (*.f64 a2 a2)) 0))
(+.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) 0)
(+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 4) (pow.f64 a2 2))) (+.f64 (pow.f64 a2 2) (+.f64 (pow.f64 a1 2) (.f64 1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4))))))))
(fma.f64 1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (fma.f64 -1/8 (/.f64 (pow.f64 a1 6) (pow.f64 a2 4)) (fma.f64 -1/4 (/.f64 (pow.f64 a1 4) (.f64 a2 a2)) (+.f64 (.f64 a2 a2) (+.f64 (.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 a2 4) (pow.f64 a1 6))))))))

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a1 a2) 4)
✓	0.2b	(pow.f64 (cos.f64 th) 2)
✓	0.3b	(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))
✓	26.3b	(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))

Compiler

Compiled 54 to 31 computations (42.6% saved)

series31.0ms (0.2%)

Counts

4 → 100

Calls

27 calls:

Time	Variable		Point	Expression
7.0ms	th	@	-inf	(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))
5.0ms	a2	@	0	(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
2.0ms	a1	@	0	(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))
1.0ms	a2	@	0	(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))
1.0ms	th	@	inf	(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))

rewrite73.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`log-prod_binary64`
354×	`pow-prod-down_binary64`
327×	`pow2_binary64`
228×	`pow-unpow_binary64`
227×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	51
1	287	48
2	3095	48

Stop Event

1×	node limit

Counts

4 → 112

Calls

Call 1

Inputs
(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
(.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4))
(pow.f64 (cos.f64 th) 2)
(pow.f64 (hypot.f64 a1 a2) 4)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))) 2)) (log.f64 (cbrt.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 +.f64 (log.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)))) (log.f64 (sqrt.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 -.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cos.f64 th) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) (cbrt.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 8) (.f64 (pow.f64 (cos.f64 th) 4) 1/4)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 12) (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) 6)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(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 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) (pow.f64 (hypot.f64 a1 a2) 4))) 2)) (log.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) (pow.f64 (hypot.f64 a1 a2) 4)))) (log.f64 (sqrt.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 6) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 8) (.f64 (pow.f64 (cos.f64 th) 4) 1/4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 12) (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2))) (hypot.f64 a1 a2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 8) (.f64 (pow.f64 (cos.f64 th) 4) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (sqrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 12) (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (sqrt.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 8) (.f64 (pow.f64 (cos.f64 th) 4) 1/4))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 12) (pow.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) 6))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (pow.f64 (cos.f64 th) 2) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (.f64 (cos.f64 th) (sqrt.f64 (*.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4))))) 1) 2))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/2 (.f64 1/2 (cos.f64 (+.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (.f64 (pow.f64 (cos.f64 th) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (cos.f64 th) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (cos.f64 th) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (cos.f64 th) 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 th) (cos.f64 th))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cos.f64 th) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (cos.f64 th) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 4) (cbrt.f64 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (cos.f64 th) 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (cos.f64 th)) (pow.f64 (cos.f64 th) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cos.f64 th) 3/2) (sqrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 5) (cbrt.f64 (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (cos.f64 (+.f64 th th)) (cos.f64 (-.f64 th th))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cos.f64 th) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (cos.f64 th) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (cos.f64 th) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (cos.f64 th) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 2 (log.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (cos.f64 th) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (pow.f64 (cos.f64 th) 2))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (cos.f64 th)) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (*.f64 2 (log.f64 (cos.f64 th))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)) (.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (hypot.f64 a1 a2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 4))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 4))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (hypot.f64 a1 a2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 (hypot.f64 a1 a2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 8)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 8) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 a1 a2) 8))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 4))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 12))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 4 (log.f64 (hypot.f64 a1 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 4 (log.f64 (hypot.f64 a1 a2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (hypot.f64 a1 a2) 12)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a1 a2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 4)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 a1 a2)) 1) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (.f64 4 (log.f64 (hypot.f64 a1 a2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (hypot.f64 a1 a2)) 2) 2))))))

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary64`
449×	`associate-/l*_binary64`
439×	`fma-def_binary64`
424×	`associate-/r*_binary64`
273×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	309	3505
1	991	3121
2	4052	2717

Stop Event

1×	node limit

Counts

212 → 194

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

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 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.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 (pow.f64 th 4) (sqrt.f64 1/2))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 th th)) -1/2))))
(+.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (+.f64 (.f64 (.f64 th th) -1/2) (.f64 (pow.f64 th 4) 1/24))))
(+.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 (pow.f64 th 4) (sqrt.f64 1/2))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 6))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (+.f64 (.f64 (.f64 th th) -1/2) (.f64 (pow.f64 th 6) -1/720))) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (+.f64 (sqrt.f64 1/2) (.f64 (.f64 (sqrt.f64 1/2) 1/24) (pow.f64 th 4)))))
(.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 (+.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 (+.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 (+.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 (+.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 (+.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 (+.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 (+.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 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (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 (.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 (sqrt.f64 1/2) (.f64 (pow.f64 a1 8) (cos.f64 th)))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (cos.f64 th)) (fma.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 (sqrt.f64 1/2) (pow.f64 a1 8)) (cos.f64 th)) (.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))))
(+.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) (pow.f64 a1 8)) (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (.f64 (/.f64 1 (pow.f64 a2 6)) 1/64)) (.f64 (cos.f64 th) (pow.f64 a1 8)))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (+.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 (sqrt.f64 1/2) (.f64 (pow.f64 a1 8) (cos.f64 th)))) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.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)))))))
(fma.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (cos.f64 th)) (fma.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 (sqrt.f64 1/2) (pow.f64 a1 8)) (cos.f64 th)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (.f64 (pow.f64 a1 12) (.f64 (cos.f64 th) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a2 8)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (.f64 a2 a2)))) (.f64 a2 a2)) (fma.f64 -1 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1/64 (pow.f64 a2 8)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (.f64 a2 a2)))) (.f64 a2 a2)) (+.f64 (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2) (/.f64 (.f64 1/8 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a2 4)))) (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10)))))))))))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th))) (fma.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (+.f64 (.f64 a2 a2) (.f64 (pow.f64 a1 12) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 -1/2 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a2 4))) (-.f64 (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10))) (fma.f64 1/2 (-.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (.f64 -1/2 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a2 4))) (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (pow.f64 (/.f64 1/16 (pow.f64 a2 5)) 2)))))))) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) (pow.f64 a1 8)) (-.f64 (/.f64 5/64 (pow.f64 a2 6)) (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))))))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (.f64 (/.f64 1 (pow.f64 a2 6)) 1/64)) (.f64 (cos.f64 th) (pow.f64 a1 8))))) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (.f64 (pow.f64 a1 12) (+.f64 (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10))) (-.f64 (.f64 (+.f64 (/.f64 1/64 (.f64 (.f64 a2 a2) (pow.f64 a2 8))) (/.f64 (*.f64 1/2 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6)))) (pow.f64 a2 4))) 0) (fma.f64 1/8 (/.f64 (+.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2) (/.f64 1/16 (pow.f64 a2 6))) (pow.f64 a2 4)) (/.f64 1/256 (pow.f64 a2 10)))))))))
(.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 (.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 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th))) (pow.f64 a1 2)) (+.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 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 (pow.f64 a2 4) 0)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) 0) a1) (/.f64 (cos.f64 th) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 1/8 (pow.f64 a2 6)) (.f64 -1/8 (pow.f64 a2 6))) (cos.f64 th))) (pow.f64 a1 4)) (+.f64 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th))) (pow.f64 a1 2)) (+.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 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 (pow.f64 a2 4) 0)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) 0) a1) (/.f64 (cos.f64 th) a1)))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) 0)
(.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 (.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 (/.f64 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (cos.f64 th))) (pow.f64 a1 2)) (+.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 (.f64 (.f64 a1 a1) (cos.f64 th)) (.f64 (.f64 a2 a2) (cos.f64 th)))) (/.f64 (sqrt.f64 1/2) (/.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (.f64 (pow.f64 a2 4) 0)))))
(fma.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (.f64 (/.f64 (.f64 (sqrt.f64 1/2) 0) a1) (/.f64 (cos.f64 th) a1)))
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(+.f64 (.f64 (pow.f64 a1 2) (.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2))) (.f64 1/2 (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2))))
(fma.f64 1/2 (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2)) (.f64 (.f64 a1 a1) (.f64 (*.f64 a2 a2) (pow.f64 (cos.f64 th) 2))))
(.f64 (pow.f64 (cos.f64 th) 2) (+.f64 (.f64 1/2 (pow.f64 a2 4)) (.f64 a2 (.f64 a2 (*.f64 a1 a1)))))
(+.f64 (.f64 (pow.f64 a1 2) (.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2))) (+.f64 (.f64 1/2 (.f64 (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 -1/2 (pow.f64 a1 4)))) (pow.f64 (cos.f64 th) 2))) (.f64 1/2 (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2)))))
(fma.f64 (.f64 a1 a1) (.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) 2)) (.f64 1/2 (+.f64 (.f64 (pow.f64 a1 4) (pow.f64 (cos.f64 th) 2)) (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2)))))
(fma.f64 1/2 (.f64 (pow.f64 (cos.f64 th) 2) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (.f64 a2 a2) (.f64 (*.f64 a1 a1) (pow.f64 (cos.f64 th) 2))))
(.f64 (pow.f64 (cos.f64 th) 2) (+.f64 (.f64 a2 (.f64 a2 (.f64 a1 a1))) (*.f64 1/2 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(+.f64 (.f64 (pow.f64 a1 2) (.f64 (pow.f64 a2 2) (pow.f64 (cos.f64 th) 2))) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a1 6)) (+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4))))) (.f64 1/4 (pow.f64 a1 6)))) (pow.f64 (cos.f64 th) 2)) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (.f64 (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (.f64 -1/2 (pow.f64 a1 4)))) (pow.f64 (cos.f64 th) 2))) (.f64 1/2 (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2))))))
(fma.f64 (.f64 a1 a1) (.f64 (.f64 a2 a2) (pow.f64 (cos.f64 th) 2)) (.f64 1/2 (+.f64 (.f64 (pow.f64 a1 4) (pow.f64 (cos.f64 th) 2)) (.f64 (pow.f64 a2 4) (pow.f64 (cos.f64 th) 2)))))
(fma.f64 1/2 (.f64 (pow.f64 (cos.f64 th) 2) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (.f64 a2 a2) (.f64 (*.f64 a1 a1) (pow.f64 (cos.f64 th) 2))))
(.f64 (pow.f64 (cos.f64 th) 2) (+.f64 (.f64 a2 (.f64 a2 (.f64 a1 a1))) (*.f64 1/2 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
1
(+.f64 1 (*.f64 -1 (pow.f64 th 2)))
(+.f64 1 (neg.f64 (*.f64 th th)))
(-.f64 1 (*.f64 th th))
(+.f64 1 (+.f64 (.f64 -1 (pow.f64 th 2)) (.f64 1/3 (pow.f64 th 4))))
(+.f64 1 (fma.f64 -1 (.f64 th th) (.f64 (pow.f64 th 4) 1/3)))
(+.f64 1 (-.f64 (.f64 (pow.f64 th 4) 1/3) (.f64 th th)))
(+.f64 (-.f64 1 (.f64 th th)) (.f64 (pow.f64 th 4) 1/3))
(+.f64 1 (+.f64 (.f64 -1 (pow.f64 th 2)) (+.f64 (.f64 -2/45 (pow.f64 th 6)) (*.f64 1/3 (pow.f64 th 4)))))
(+.f64 1 (fma.f64 -1 (.f64 th th) (fma.f64 -2/45 (pow.f64 th 6) (.f64 (pow.f64 th 4) 1/3))))
(+.f64 1 (-.f64 (fma.f64 (pow.f64 th 4) 1/3 (.f64 (pow.f64 th 6) -2/45)) (.f64 th th)))
(+.f64 (-.f64 1 (.f64 th th)) (fma.f64 (pow.f64 th 4) 1/3 (.f64 (pow.f64 th 6) -2/45)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (.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) (pow.f64 a2 2)))) (pow.f64 a2 4))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4)) (fma.f64 2 (.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 a2 a2) (pow.f64 a1 8))) (pow.f64 a2 4)))
(+.f64 (fma.f64 2 (.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 a2 (.f64 a2 (pow.f64 a1 8)))) (pow.f64 a2 4)) (fma.f64 2 (.f64 a2 (.f64 a2 (.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (fma.f64 2 (.f64 (+.f64 (neg.f64 (pow.f64 (/.f64 -1/8 (pow.f64 a2 3)) 2)) (.f64 (/.f64 1 (pow.f64 a2 6)) 1/64)) (.f64 a2 (.f64 a2 (pow.f64 a1 8)))) (pow.f64 a2 4)) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/2 (pow.f64 a2 4)) (+.f64 (.f64 1/2 (pow.f64 a2 4)) (pow.f64 a2 4)))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 6) (pow.f64 a1 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 6) (pow.f64 a1 2))) (+.f64 (.f64 -1/2 (pow.f64 a2 4)) (+.f64 (.f64 1/2 (pow.f64 a2 4)) (+.f64 (pow.f64 a2 4) (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)) (pow.f64 a1 2))))))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 -1/2 (pow.f64 a2 4)) (+.f64 (.f64 1/2 (pow.f64 a2 4)) (pow.f64 a2 4)))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a2 6) (pow.f64 a1 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a2 6) (pow.f64 a1 2))) (+.f64 (.f64 -1/2 (pow.f64 a2 4)) (+.f64 (.f64 1/2 (pow.f64 a2 4)) (+.f64 (pow.f64 a2 4) (.f64 2 (/.f64 (.f64 (+.f64 (.f64 -1/4 (pow.f64 a2 4)) (.f64 1/4 (pow.f64 a2 4))) (pow.f64 a2 2)) (pow.f64 a1 2))))))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(pow.f64 a1 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a1 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (pow.f64 a2 4) (.f64 2 (.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 a1 2) (pow.f64 a2 8)))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 a1 4)) (+.f64 (pow.f64 a2 4) (.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 (*.f64 a1 a1) (pow.f64 a2 8))))))
(+.f64 (fma.f64 2 (.f64 a2 (.f64 a2 (.f64 a1 a1))) (pow.f64 a1 4)) (fma.f64 2 (.f64 (.f64 a1 a1) (.f64 (pow.f64 a2 8) (-.f64 (/.f64 5/64 (pow.f64 a1 6)) (+.f64 (/.f64 1/16 (pow.f64 a1 6)) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))))) (pow.f64 a2 4)))
(+.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (.f64 (.f64 a1 a1) (+.f64 (.f64 (.f64 2 (-.f64 (.f64 (/.f64 1 (pow.f64 a1 6)) 1/64) (pow.f64 (/.f64 -1/8 (pow.f64 a1 3)) 2))) (pow.f64 a2 8)) (.f64 2 (*.f64 a2 a2)))))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (+.f64 (pow.f64 a2 4) (.f64 -1/2 (pow.f64 a1 4))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 6) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 6) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (+.f64 (pow.f64 a2 4) (.f64 -1/2 (pow.f64 a1 4)))))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(pow.f64 a2 4)
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (pow.f64 a2 4))
(fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a2 4))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (+.f64 (pow.f64 a2 4) (.f64 -1/2 (pow.f64 a1 4))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))
(+.f64 (.f64 2 (.f64 (pow.f64 a1 2) (pow.f64 a2 2))) (+.f64 (.f64 1/4 (/.f64 (pow.f64 a1 6) (pow.f64 a2 2))) (+.f64 (.f64 -1/4 (/.f64 (pow.f64 a1 6) (pow.f64 a2 2))) (+.f64 (pow.f64 a1 4) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 a1 2) (+.f64 (.f64 -1/4 (pow.f64 a1 4)) (.f64 1/4 (pow.f64 a1 4)))) (pow.f64 a2 2))) (+.f64 (.f64 1/2 (pow.f64 a1 4)) (+.f64 (pow.f64 a2 4) (.f64 -1/2 (pow.f64 a1 4)))))))))
(+.f64 (fma.f64 2 (.f64 (.f64 a2 a2) (*.f64 a1 a1)) (pow.f64 a1 4)) (pow.f64 a2 4))
(fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(+.f64 (pow.f64 a2 4) (fma.f64 2 (.f64 a2 (.f64 a2 (*.f64 a1 a1))) (pow.f64 a1 4)))

eval417.0ms (2.4%)

Compiler: Compiled 14543 to 9678 computations (33.5% saved)

prune234.0ms (1.4%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	671	22	693
Fresh	8	0	8
Picked	1	0	1
Done	4	1	5
Total	684	23	707

Error

Counts

707 → 23

Alt Table

Click to see full alt table

Status	Error	Program
	30.5b	(.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	25.2b	(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
	25.2b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
	44.5b	(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (.f64 th (.f64 th -1/2))))
	25.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
▶	29.4b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	41.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	30.5b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
	43.8b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
▶	41.1b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
▶	25.2b	(.f64 a2 (.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
	45.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	25.2b	(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
▶	43.7b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
▶	29.4b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
	31.0b	(pow.f64 (/.f64 (sqrt.f64 2) (.f64 a1 (.f64 a1 (cos.f64 th)))) -1)
	30.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	30.5b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
✓	25.2b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.2b	(.f64 (.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	30.5b	(.f64 (/.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (sqrt.f64 2)) 1)
	30.5b	(.f64 (cos.f64 th) (.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))
	30.5b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 556 to 425 computations (23.6% saved)

localize34.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 35 to 24 computations (31.4% saved)

series16.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	th	@	inf	(.f64 a2 (.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
1.0ms	a2	@	0	(*.f64 (pow.f64 2 -1/2) a2)
1.0ms	a2	@	inf	(.f64 a2 (.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
1.0ms	a2	@	inf	(*.f64 (pow.f64 2 -1/2) a2)
1.0ms	th	@	-inf	(.f64 (.f64 (pow.f64 2 -1/2) a2) (cos.f64 th))

rewrite82.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

949×	`pow1_binary64`
876×	`add-log-exp_binary64`
875×	`log1p-expm1-u_binary64`
875×	`expm1-log1p-u_binary64`
856×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	208	31
2	2426	31

Stop Event

1×	node limit

Counts

3 → 39

Calls

Call 1

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

Outputs

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

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

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

simplify244.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

841×	`distribute-lft-out_binary64`
697×	`sqr-pow_binary64`
645×	`*-commutative_binary64`
524×	`distribute-rgt-in_binary64`
368×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	830
1	143	830
2	410	790
3	1763	769
4	3229	758
5	3851	758
6	4498	758
7	5464	758
8	5621	758
9	5804	758
10	6095	758
11	6397	758
12	6738	758
13	7148	758
14	7633	758

Stop Event

1×	node limit

Counts

99 → 59

Calls

Call 1

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

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

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series5.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite65.0ms (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	15
1	127	15
2	1566	15

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify110.0ms (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

62 → 52

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite47.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`pow1_binary64`
535×	`add-log-exp_binary64`
535×	`log1p-expm1-u_binary64`
535×	`expm1-log1p-u_binary64`
522×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	129	9
2	1504	9

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 26 to 11 computations (57.7% saved)

series6.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

674×	`pow1_binary64`
620×	`add-log-exp_binary64`
620×	`log1p-expm1-u_binary64`
620×	`expm1-log1p-u_binary64`
605×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	158	12
2	1753	12

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

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

simplify187.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1040×	`sqr-pow_binary64`
784×	`cube-prod_binary64`
743×	`fabs-mul_binary64`
484×	`unswap-sqr_binary64`
360×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	324
1	25	288
2	49	288
3	94	288
4	226	288
5	687	288
6	1068	288
7	1891	288
8	2108	288
9	2348	288
10	2661	288
11	3107	288
12	3703	288
13	4412	288
14	5296	288
15	5988	288
16	6446	288
17	6882	288
18	7038	288
19	7108	288
20	7935	288

Stop Event

1×	node limit

Counts

39 → 21

Calls

Call 1

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

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

localize19.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 26 to 11 computations (57.7% saved)

series5.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

765×	`pow1_binary64`
708×	`add-log-exp_binary64`
708×	`log1p-expm1-u_binary64`
708×	`expm1-log1p-u_binary64`
691×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	164	12
2	1958	12

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

780×	`associate-/r/_binary64`
600×	`associate-/l/_binary64`
600×	`sqr-pow_binary64`
566×	`*-commutative_binary64`
372×	`cube-prod_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	414
1	19	414
2	32	414
3	62	378
4	150	378
5	513	378
6	2172	378
7	3474	378
8	3900	378
9	4183	378
10	4528	378
11	5111	378
12	6228	378
13	7562	378

Stop Event

1×	node limit

Counts

55 → 37

Calls

Call 1

Inputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))

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

eval104.0ms (0.6%)

Compiler: Compiled 2290 to 1621 computations (29.2% saved)

prune123.0ms (0.7%)

Pruning

37 alts after pruning (33 fresh and 4 done)

	Pruned	Kept	Total
New	179	20	199
Fresh	4	13	17
Picked	0	1	1
Done	2	3	5
Total	185	37	222

Error

Counts

222 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	43.8b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	44.9b	(.f64 a2 (.f64 (sqrt.f64 1/2) (+.f64 a2 (.f64 th (.f64 -1/2 (*.f64 a2 th))))))
	30.5b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
	44.0b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	48.3b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
✓	25.2b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.2b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
	48.6b	(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
	30.5b	(.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	44.5b	(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (.f64 th (.f64 th -1/2))))
	41.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	30.5b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
	43.8b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	41.2b	(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	48.1b	(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
	43.8b	(.f64 a1 (.f64 (pow.f64 2 -1/2) a1))
	43.7b	(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
▶	44.5b	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
	41.2b	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
	54.4b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	45.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	25.2b	(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
	30.5b	(.f64 (/.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (sqrt.f64 2)) 1)
	41.2b	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
▶	41.2b	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
	30.5b	(.f64 (cos.f64 th) (.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))
	41.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
▶	41.1b	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)
▶	25.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
✓	43.7b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
▶	25.2b	(.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th)))
✓	29.4b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
	43.7b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	29.4b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	43.8b	(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
	30.5b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
	30.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Compiler

Compiled 839 to 658 computations (21.6% saved)

localize31.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 30 to 19 computations (36.7% saved)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	a2	@	-inf	(*.f64 (sqrt.f64 1/2) a2)
1.0ms	a2	@	inf	(*.f64 (sqrt.f64 1/2) a2)
1.0ms	a2	@	0	(*.f64 (sqrt.f64 1/2) a2)
1.0ms	th	@	0	(.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th)))
1.0ms	th	@	0	(.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))

rewrite78.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

844×	`pow1_binary64`
775×	`add-log-exp_binary64`
775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
757×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	181	31
2	2128	31

Stop Event

1×	node limit

Counts

3 → 39

Calls

Call 1

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

Outputs

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

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

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

simplify251.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

835×	`distribute-lft-out_binary64`
697×	`sqr-pow_binary64`
651×	`*-commutative_binary64`
524×	`distribute-rgt-in_binary64`
368×	`pow-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	56	758
1	144	758
2	411	718
3	1768	697
4	3235	686
5	3860	686
6	4495	686
7	5461	686
8	5618	686
9	5801	686
10	6092	686
11	6390	686
12	6735	686
13	7143	686
14	7626	686

Stop Event

1×	node limit

Counts

87 → 59

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

localize18.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

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 (sqrt.f64 1/2) a2))
1.0ms	a2	@	inf	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
0.0ms	a2	@	-inf	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`pow1_binary64`
490×	`add-sqr-sqrt_binary64`
471×	`add-log-exp_binary64`
471×	`log1p-expm1-u_binary64`
471×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	120	9
2	1316	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify194.0ms (1.1%)

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))

localize23.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 16 computations (36% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite68.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`pow1_binary64`
570×	`add-log-exp_binary64`
570×	`log1p-expm1-u_binary64`
570×	`expm1-log1p-u_binary64`
556×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	127	9
2	1583	9

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

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

Outputs

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

simplify123.0ms (0.7%)

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

44 → 34

Calls

Call 1

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

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)))

localize43.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2))))
✓	11.4b	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))

Compiler

Compiled 52 to 36 computations (30.8% saved)

series11.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	a2	@	0	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
2.0ms	th	@	inf	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
1.0ms	a2	@	inf	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
1.0ms	th	@	0	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
1.0ms	th	@	0	(.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2))))

rewrite110.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

632×	`log-prod_binary64`
559×	`prod-diff_binary64`
404×	`fma-def_binary64`
316×	`pow2_binary64`
249×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	271	32
2	3362	32

Stop Event

1×	node limit

Counts

2 → 130

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 a2 (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 (*.f64 a2 a2) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 th (*.f64 th -1/2)) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) 1) (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 th (*.f64 th -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 th (*.f64 th -1/2))) (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 a2) (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 a2) (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a2) (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 a2) (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 (*.f64 (*.f64 a2 (sqrt.f64 1/2)) (fma.f64 th (*.f64 th -1/2) 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (fma.f64 (pow.f64 (*.f64 th th) 3) -1/8 1)) (fma.f64 (*.f64 th (*.f64 th -1/2)) (fma.f64 th (*.f64 th 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-1/2) 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (fma.f64 th (*.f64 th -1/2) 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 th (*.f64 th -1/2) 1) 3) (*.f64 1/2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 th (*.f64 th -1/2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 th (*.f64 th -1/2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 th (*.f64 th -1/2) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 1/2) (fma.f64 th (*.f64 th -1/2) 1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) 1 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) 1 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 1/2) (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (sqrt.f64 1/2) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 th (*.f64 (*.f64 th -1/2) (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th -1/2) (*.f64 th (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th (*.f64 th -1/2)) (sqrt.f64 1/2) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th th) (*.f64 -1/2 (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (cbrt.f64 (sqrt.f64 1/2)) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (cbrt.f64 (sqrt.f64 1/2)) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) (*.f64 th (*.f64 th -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) 1) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 1/2) (*.f64 (cbrt.f64 (sqrt.f64 1/2)) 1) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 (*.f64 th th) 2) 1/4)) (*.f64 (cbrt.f64 (*.f64 th (*.f64 th -1/2))) (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (pow.f64 1/2 1/4) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (pow.f64 1/2 1/4) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) (*.f64 th (*.f64 th -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) 1) (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 1/2 1/4) (*.f64 (pow.f64 1/2 1/4) 1) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 th (sqrt.f64 -1/2)) (*.f64 (*.f64 th (sqrt.f64 -1/2)) (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2))) 2) (cbrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2))) (sqrt.f64 (*.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 th (sqrt.f64 -1/2)) (pow.f64 1/2 1/4)) (*.f64 (*.f64 th (sqrt.f64 -1/2)) (pow.f64 1/2 1/4)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (pow.f64 1/2 1/4) (*.f64 th (sqrt.f64 -1/2))) (*.f64 (pow.f64 1/2 1/4) (*.f64 th (sqrt.f64 -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 th (*.f64 th -1/2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 1/2)) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (*.f64 th (*.f64 th -1/2)) (pow.f64 1/2 1/4)) (pow.f64 1/2 1/4) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) th) (*.f64 th -1/2) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 th -1/2)) th (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 th th)) -1/2 (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (cbrt.f64 (*.f64 (pow.f64 (*.f64 th th) 2) 1/4))) (cbrt.f64 (*.f64 th (*.f64 th -1/2))) (sqrt.f64 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (sqrt.f64 1/2) (*.f64 th (sqrt.f64 -1/2))) (*.f64 th (sqrt.f64 -1/2)) (sqrt.f64 1/2))))))

simplify219.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1094×	`distribute-rgt-in_binary64`
872×	`distribute-lft-in_binary64`
729×	`fma-def_binary64`
641×	`associate-l_binary64`
458×	`sqr-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	648
1	49	606
2	129	588
3	503	588
4	2364	588
5	3203	588
6	3759	588
7	4355	588
8	5360	588
9	5495	588
10	5651	588
11	5821	588
12	6019	588
13	6243	588
14	7521	588

Stop Event

1×	node limit

Counts

166 → 142

Calls

Call 1

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

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

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 29 to 12 computations (58.6% saved)

series8.0ms (0%)

Counts

3 → 64

Calls

18 calls:

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

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`pow1_binary64`
760×	`add-log-exp_binary64`
760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
743×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	180	29
2	2092	29

Stop Event

1×	node limit

Counts

3 → 39

Calls

Call 1

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

Outputs

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

((#(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 (cos.f64 th)) a2))))) (#(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))))))))

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

simplify195.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

752×	`*-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	164	825
2	480	772
3	1967	747
4	3760	747
5	4017	747
6	4246	747
7	4481	747
8	4816	747
9	5421	747
10	5985	747
11	6288	747
12	6629	747
13	7037	747
14	7520	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) 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)))
(*.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))

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

eval118.0ms (0.7%)

Compiler: Compiled 5143 to 3567 computations (30.6% saved)

prune77.0ms (0.5%)

Pruning

42 alts after pruning (33 fresh and 9 done)

	Pruned	Kept	Total
New	324	7	331
Fresh	2	26	28
Picked	0	1	1
Done	0	8	8
Total	326	42	368

Error

Counts

368 → 42

Alt Table

Click to see full alt table

Status	Error	Program
	43.8b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	44.9b	(.f64 a2 (.f64 (sqrt.f64 1/2) (+.f64 a2 (.f64 th (.f64 -1/2 (*.f64 a2 th))))))
	30.5b	(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
	44.0b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	48.3b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
✓	25.2b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.2b	(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
	48.6b	(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
	30.5b	(.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	44.5b	(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (.f64 th (.f64 th -1/2))))
	45.4b	(.f64 a2 (-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) a2)) 1))
	41.2b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	57.7b	(.f64 (.f64 a2 a2) (.f64 th (.f64 th (*.f64 -1/2 (sqrt.f64 1/2)))))
	30.5b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
	43.8b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	41.2b	(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	48.1b	(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
	43.8b	(.f64 a1 (.f64 (pow.f64 2 -1/2) a1))
	43.7b	(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
✓	44.5b	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
	41.2b	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
	54.4b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	45.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	41.2b	(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
	30.5b	(.f64 (/.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (sqrt.f64 2)) 1)
	41.2b	(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
✓	41.2b	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
	58.1b	(.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 th a2) (*.f64 th a2))))
	35.1b	(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))) 1)
	43.8b	(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
	30.5b	(.f64 (cos.f64 th) (.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))
✓	41.1b	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)
✓	25.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	41.2b	(.f64 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1) 1)
✓	43.7b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
✓	25.2b	(.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th)))
✓	29.4b	(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
	30.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	41.2b	(.f64 (.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2))) 1)
	43.7b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	29.4b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	30.5b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))

Compiler

Compiled 515 to 402 computations (21.9% saved)

regimes351.0ms (2.1%)

Counts

64 → 1

Calls

Call 1

Inputs
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(.f64 a1 (.f64 (pow.f64 2 -1/2) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)
(.f64 a2 (-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) a2)) 1))
(.f64 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1) 1)
(.f64 (.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2))) 1)
(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
(-.f64 (+.f64 1 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1)
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(.f64 (.f64 a2 a2) (.f64 th (.f64 th (*.f64 -1/2 (sqrt.f64 1/2)))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (.f64 th a2) (*.f64 th a2))))
(.f64 a2 (.f64 (sqrt.f64 1/2) (+.f64 a2 (.f64 th (.f64 -1/2 (*.f64 a2 th))))))
(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 th (*.f64 th -1/2)))))
(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (+.f64 1 (.f64 th (.f64 th -1/2))))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th)))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(.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 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th))
(.f64 (.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (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 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
(.f64 a2 (.f64 (*.f64 (pow.f64 2 -1/2) a2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (*.f64 a1 a1) (pow.f64 2 -1/2)))
(.f64 (/.f64 (.f64 a1 (*.f64 a1 (cos.f64 th))) (sqrt.f64 2)) 1)
(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))) 1)
(.f64 (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(/.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 (/.f64 (sqrt.f64 2) (.f64 a1 (.f64 a1 (cos.f64 th)))) -1)
(.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 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (fma.f64 a1 a1 (.f64 a2 a2)))
(/.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (pow.f64 2 1/4))

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

Calls

10 calls:

41.0ms	th
40.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
38.0ms	a2
37.0ms	a1
35.0ms	(cos.f64 th)

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)`

Compiler

Compiled 706 to 436 computations (38.2% saved)

regimes232.0ms (1.4%)

Counts

55 → 1

Calls

Call 1

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

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

Calls

8 calls:

36.0ms	a1
33.0ms	th
31.0ms	a2
30.0ms	(cos.f64 th)
26.0ms	(/.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 552 to 345 computations (37.5% saved)

regimes712.0ms (4.2%)

Counts

54 → 2

Calls

Call 1

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

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

Calls

7 calls:

241.0ms	th
116.0ms	(*.f64 a1 a1)
81.0ms	(cos.f64 th)
69.0ms	(*.f64 a2 a2)
69.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.3b	2	`a1`
7.2b	2	`a2`
12.9b	5	`th`
14.7b	2	`(cos.f64 th)`
9.5b	6	`(*.f64 a1 a1)`
9.6b	4	`(*.f64 a2 a2)`
9.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 532 to 333 computations (37.4% saved)

bsearch64.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
63.0ms	-6.895388867423736e-118	-5.466196423826453e-131

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes544.0ms (3.2%)

Counts

46 → 2

Calls

Call 1

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

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

Calls

8 calls:

146.0ms	th
65.0ms	(*.f64 a1 a1)
59.0ms	(*.f64 a1 a1)
53.0ms	a2
52.0ms	a1

Results

Error	Segments	Branch
6.3b	2	`a1`
7.2b	2	`a2`
12.9b	5	`th`
14.7b	2	`(cos.f64 th)`
9.5b	6	`(*.f64 a1 a1)`
9.5b	6	`(*.f64 a1 a1)`
9.6b	4	`(*.f64 a2 a2)`
9.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 453 to 288 computations (36.4% saved)

bsearch62.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
62.0ms	-6.895388867423736e-118	-5.466196423826453e-131

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes589.0ms (3.5%)

Counts

41 → 2

Calls

Call 1

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

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

Calls

8 calls:

167.0ms	a2
120.0ms	th
57.0ms	(*.f64 a1 a1)
54.0ms	(*.f64 a1 a1)
50.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.3b	2	`a1`
7.2b	2	`a2`
12.9b	5	`th`
14.7b	2	`(cos.f64 th)`
9.5b	6	`(*.f64 a1 a1)`
9.5b	6	`(*.f64 a1 a1)`
9.6b	4	`(*.f64 a2 a2)`
9.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 407 to 264 computations (35.1% saved)

bsearch63.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
62.0ms	-6.895388867423736e-118	-5.466196423826453e-131

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes633.0ms (3.7%)

Counts

39 → 2

Calls

Call 1

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

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

Calls

8 calls:

193.0ms	th
88.0ms	(cos.f64 th)
80.0ms	a1
67.0ms	a2
53.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
6.3b	2	`a1`
7.3b	2	`a2`
12.9b	5	`th`
14.7b	2	`(cos.f64 th)`
9.5b	6	`(*.f64 a1 a1)`
9.5b	6	`(*.f64 a1 a1)`
9.6b	4	`(*.f64 a2 a2)`
9.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 389 to 255 computations (34.4% saved)

bsearch133.0ms (0.8%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
133.0ms	-6.895388867423736e-118	-5.466196423826453e-131

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes748.0ms (4.4%)

Counts

38 → 2

Calls

Call 1

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

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

Calls

8 calls:

186.0ms	th
108.0ms	(*.f64 a2 a2)
80.0ms	(*.f64 a1 a1)
71.0ms	(*.f64 a1 a1)
69.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.3b	2	`a1`
7.3b	2	`a2`
12.9b	5	`th`
14.7b	2	`(cos.f64 th)`
9.5b	6	`(*.f64 a1 a1)`
9.5b	6	`(*.f64 a1 a1)`
9.6b	4	`(*.f64 a2 a2)`
9.6b	4	`(*.f64 a2 a2)`

Compiler

Compiled 380 to 251 computations (33.9% saved)

bsearch78.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
78.0ms	-6.895388867423736e-118	-5.466196423826453e-131

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes299.0ms (1.7%)

Counts

36 → 3

Calls

Call 1

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

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

Calls

7 calls:

75.0ms	th
50.0ms	(*.f64 a1 a1)
37.0ms	a2
36.0ms	a1
29.0ms	(cos.f64 th)

Results

Error	Segments	Branch
17.1b	2	`a1`
16.6b	2	`a2`
14.7b	3	`th`
14.7b	2	`(cos.f64 th)`
19.7b	2	`(*.f64 a1 a1)`
18.5b	2	`(*.f64 a2 a2)`
18.5b	2	`(*.f64 a2 a2)`

Compiler

Compiled 356 to 239 computations (32.9% saved)

bsearch74.0ms (0.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
37.0ms	1.4566389604854082e-16	1.7120722258190529e-9
37.0ms	-0.007453308212503148	-1.6985407511627086e-12

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes477.0ms (2.8%)

Counts

35 → 2

Calls

Call 1

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

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

Calls

8 calls:

183.0ms	th
118.0ms	a2
55.0ms	a1
29.0ms	(*.f64 a2 a2)
28.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
18.8b	2	`a1`
16.7b	2	`a2`
22.5b	5	`th`
25.2b	1	`(cos.f64 th)`
20.9b	2	`(*.f64 a1 a1)`
20.9b	2	`(*.f64 a1 a1)`
19.4b	2	`(*.f64 a2 a2)`
19.4b	2	`(*.f64 a2 a2)`

Compiler

Compiled 353 to 239 computations (32.3% saved)

bsearch59.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
59.0ms	2.0915784599899e-166	2.283291334674652e-161

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes358.0ms (2.1%)

Counts

31 → 2

Calls

Call 1

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

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

Calls

8 calls:

136.0ms	th
52.0ms	a1
51.0ms	a2
28.0ms	(*.f64 a2 a2)
27.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
18.8b	2	`a1`
16.7b	2	`a2`
22.5b	5	`th`
25.2b	1	`(cos.f64 th)`
20.9b	2	`(*.f64 a1 a1)`
20.9b	2	`(*.f64 a1 a1)`
19.5b	2	`(*.f64 a2 a2)`
19.5b	2	`(*.f64 a2 a2)`

Compiler

Compiled 317 to 222 computations (30% saved)

bsearch89.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
89.0ms	2.0915784599899e-166	2.283291334674652e-161

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes266.0ms (1.6%)

Counts

30 → 2

Calls

Call 1

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

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

Calls

6 calls:

80.0ms	th
41.0ms	(*.f64 a2 a2)
36.0ms	(*.f64 a1 a1)
34.0ms	a1
30.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
31.4b	2	`a1`
32.6b	2	`a2`
38.5b	5	`th`
34.8b	2	`(*.f64 a1 a1)`
34.8b	2	`(*.f64 a1 a1)`
34.6b	2	`(*.f64 a2 a2)`

Compiler

Compiled 297 to 208 computations (30% saved)

bsearch64.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
64.0ms	-3.0393027398314696e-136	-8.990438045660026e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes128.0ms (0.8%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

7 calls:

43.0ms	th
16.0ms	(*.f64 a2 a2)
16.0ms	a2
14.0ms	(*.f64 a2 a2)
13.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
31.4b	2	`a1`
32.7b	2	`a2`
38.5b	5	`th`
34.8b	2	`(*.f64 a1 a1)`
34.8b	2	`(*.f64 a1 a1)`
34.7b	2	`(*.f64 a2 a2)`
34.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 110 to 72 computations (34.5% saved)

bsearch76.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
76.0ms	-3.0393027398314696e-136	-8.990438045660026e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes95.0ms (0.6%)

Counts

7 → 2

Calls

Call 1

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

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

Calls

6 calls:

31.0ms	th
15.0ms	a2
14.0ms	(*.f64 a2 a2)
13.0ms	(*.f64 a1 a1)
11.0ms	a1

Results

Error	Segments	Branch
31.4b	2	`a1`
32.7b	2	`a2`
38.5b	5	`th`
34.8b	2	`(*.f64 a1 a1)`
34.7b	2	`(*.f64 a2 a2)`
34.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 75 to 50 computations (33.3% saved)

bsearch70.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
70.0ms	-3.0393027398314696e-136	-8.990438045660026e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes75.0ms (0.4%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

6 calls:

23.0ms	th
13.0ms	(*.f64 a2 a2)
11.0ms	(*.f64 a1 a1)
10.0ms	a1
8.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
31.4b	2	`a1`
32.7b	2	`a2`
38.5b	5	`th`
34.8b	2	`(*.f64 a1 a1)`
34.7b	2	`(*.f64 a2 a2)`
34.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 57 to 39 computations (31.6% saved)

bsearch67.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
67.0ms	-3.0393027398314696e-136	-8.990438045660026e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes54.0ms (0.3%)

Accuracy

Total -24.1b remaining (-76.5%)

Threshold costs -24.1b (-76.5%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

19.0ms	th
12.0ms	a1
9.0ms	(*.f64 a2 a2)
6.0ms	(*.f64 a1 a1)
6.0ms	a2

Results

Error	Segments	Branch
31.4b	2	`a1`
32.7b	2	`a2`
38.5b	5	`th`
34.8b	2	`(*.f64 a1 a1)`
34.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 39 to 28 computations (28.2% saved)

bsearch66.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
65.0ms	-3.0393027398314696e-136	-8.990438045660026e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify20.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	76	448
1	103	448

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 2 -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)))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (cos.f64 th) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th)) (.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 th -137489269098523184/18446744073709551616) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))) (if (<=.f64 th 2954414804120243/20282409603651670423947251286016) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))))
(if (<=.f64 a2 222183357011564064/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a2 222183357011564064/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) 1))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))

Outputs
(.f64 (.f64 (pow.f64 2 -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 (fma.f64 a1 a1 (.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (cos.f64 th) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -3915496599937811/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552) (.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1))) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -3915496599937811/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 (cos.f64 th) a1))) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (cos.f64 th)) (.f64 a2 (.f64 (*.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -3915496599937811/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552) (.f64 (cos.f64 th) (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) (.f64 a2 (.f64 (cos.f64 th) (*.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -3915496599937811/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 a1 -501183564792039808/726838724295606890549323807888004534353641360687318060281490199180639288113397923326191050713763565560762521606266177933534601628614656) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a1 -3915496599937811/5678427533559428832416592249125035424637823130369672345949142181098744438385921275985867583701277855943457200048954515105739075223552) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 th -137489269098523184/18446744073709551616) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))) (if (<=.f64 th 2954414804120243/20282409603651670423947251286016) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))))
(if (<=.f64 th -8593079318657699/1152921504606846976) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))) (if (<=.f64 th 2954414804120243/20282409603651670423947251286016) (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))))
(if (<=.f64 a2 222183357011564064/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (.f64 (.f64 (sqrt.f64 1/2) a2) (cos.f64 th))))
(if (<=.f64 a2 6943229906611377/33196124551047943668099262909529289208099569857939495199965258637525222491303265171197656391576830354305583092890406313459161208603294202463094998672911709496489454427212076189483008) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (.f64 (cos.f64 th) (.f64 a2 (sqrt.f64 1/2)))))
(if (<=.f64 a2 222183357011564064/1062275985633534197379176413104937254659186235454063846398888276400807119721704485478325004530458571337778658972493002030693158675305414478819039957533174703887662541670786438063456256) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 6943229906611377/33196124551047943668099262909529289208099569857939495199965258637525222491303265171197656391576830354305583092890406313459161208603294202463094998672911709496489454427212076189483008) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 (cos.f64 th) a2))))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) 1))
(if (<=.f64 a1 -7959060034493875/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -7959060034493875/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -7959060034493875/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -7959060034493875/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -4075038737660864000/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a1 -7959060034493875/26187124863169134960105517574620793217733136368344518315866330944769070371237396439066160738607233257207093473020480568073738052367083144426628220715008) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))

Compiler

Compiled 343 to 241 computations (29.7% saved)

soundness13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 53 to 36 computations (32.1% saved)

end158.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 330 to 200 computations (39.4% saved)