Details

analyze379.0ms (2.2%)

Algorithm

1×

Search

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

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample5.4s (31.4%)

Results

1.5s	1916×	body	1024	valid
1.4s	5397×	body	256	valid
1.2s	1593×	body	1024	invalid
459.0ms	1469×	body	256	invalid
427.0ms	936×	body	512	valid
396.0ms	857×	body	512	invalid
6.0ms	7×	body	2048	valid
1.0ms	1×	body	2048	invalid

preprocess56.0ms (0.3%)

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)

simplify10.0ms (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)

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.5b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Compiler

Compiled 37 to 25 computations (32.4% saved)

localize31.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series19.0ms (0.1%)

Counts

3 → 64

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	th	@	-inf	(/.f64 (cos.f64 th) (sqrt.f64 2))
2.0ms	th	@	0	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
2.0ms	th	@	0	(/.f64 (cos.f64 th) (sqrt.f64 2))
2.0ms	a2	@	-inf	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
1.0ms	th	@	inf	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite103.0ms (0.6%)

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	34
1	224	32
2	2738	32

Stop Event

1×	node limit

Counts

3 → 122

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

Outputs

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

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

simplify61.0ms (0.4%)

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	1129
1	145	1025
2	373	1021
3	1196	989
4	4370	974

Stop Event

1×	node limit

Counts

186 → 151

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)))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a1 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))

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

localize121.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 59 to 29 computations (50.8% saved)

series18.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	283	46
2	3917	45

Stop Event

1×	node limit

Counts

3 → 147

Calls

Call 1

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

Inputs

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

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

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

Outputs
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Outputs

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

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

751×	`associate-+l+_binary64`
730×	`associate-/l*_binary64`
509×	`associate-+r+_binary64`
509×	`associate-/r*_binary64`
442×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

231 → 178

Calls

Call 1

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

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

eval331.0ms (1.9%)

Compiler: Compiled 9735 to 5608 computations (42.4% saved)

prune95.0ms (0.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	421	16	437
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	423	16	439

Error

Counts

439 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	32.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
▶	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
▶	18.0b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
	0.4b	(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	28.1b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
▶	25.1b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	33.1b	(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
	1.7b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) (fma.f64 a1 a1 (.f64 a2 a2)))
	27.4b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
	27.4b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
▶	28.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	28.1b	(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
	27.4b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))

Compiler

Compiled 466 to 348 computations (25.3% saved)

localize90.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 42 to 25 computations (40.5% saved)

series60.0ms (0.4%)

Counts

4 → 108

Calls

27 calls:

Time	Variable		Point	Expression
17.0ms	a2	@	0	(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
8.0ms	a1	@	0	(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
4.0ms	a2	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
4.0ms	a1	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
3.0ms	a2	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))

rewrite84.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`log-prod_binary64`
413×	`exp-prod_binary64`
388×	`prod-exp_binary64`
336×	`pow-prod-down_binary64`
298×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	249	40
2	2788	40

Stop Event

1×	node limit

Counts

4 → 142

Calls

Call 1

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

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

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

878×	`times-frac_binary64`
840×	`distribute-rgt-in_binary64`
826×	`distribute-lft-in_binary64`
413×	`fma-def_binary64`
224×	`associate-+r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	299	3748
1	976	3330
2	3593	2839

Stop Event

1×	node limit

Counts

250 → 236

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

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

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
✓	0.2b	(*.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)

series10.0ms (0.1%)

Counts

3 → 48

Calls

15 calls:

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

rewrite66.0ms (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 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th))
(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))

Outputs

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

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

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

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

117 → 89

Calls

Call 1

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

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

localize11.0ms (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)

series4.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite56.0ms (0.3%)

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))))))))

simplify124.0ms (0.7%)

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)))

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 37 to 16 computations (56.8% saved)

series10.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

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

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	224	17
2	2729	17

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify56.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	1089
1	106	1073
2	286	939
3	1022	725
4	3906	712

Stop Event

1×	node limit

Counts

74 → 54

Calls

Call 1

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

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

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 47 to 27 computations (42.6% saved)

series27.0ms (0.2%)

Counts

3 → 76

Calls

21 calls:

Time	Variable		Point	Expression
11.0ms	th	@	0	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
1.0ms	a2	@	inf	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
1.0ms	a1	@	inf	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
1.0ms	a2	@	0	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
1.0ms	a1	@	0	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
420×	`exp-prod_binary64`
351×	`pow-prod-down_binary64`
296×	`pow2_binary64`
215×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	250	43
2	2956	43

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

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

Outputs

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

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

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

981×	`times-frac_binary64`
591×	`associate-/l*_binary64`
574×	`associate-/r*_binary64`
467×	`associate-*l/_binary64`
418×	`associate-*r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	3616
1	706	3294
2	2643	2774

Stop Event

1×	node limit

Counts

183 → 186

Calls

Call 1

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

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

eval719.0ms (4.2%)

Compiler: Compiled 15511 to 10534 computations (32.1% saved)

prune268.0ms (1.6%)

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	693	17	710
Fresh	9	2	11
Picked	1	0	1
Done	1	3	4
Total	704	22	726

Error

Counts

726 → 22

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
✓	28.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	25.1b	(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
✓	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	27.4b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (pow.f64 2 -1/2) (cos.f64 th)))
	28.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	27.4b	(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
	44.8b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	28.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
▶	40.6b	(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
	40.6b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
▶	39.3b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	27.4b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
	39.3b	(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
	27.4b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
	27.4b	(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
	27.4b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
✓	25.1b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
▶	28.1b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
▶	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	36.1b	(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) 2)

Compiler

Compiled 509 to 389 computations (23.6% saved)

localize35.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 51 to 21 computations (58.8% saved)

series36.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
24.0ms	a1	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	a2	@	0	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
1.0ms	th	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	th	@	-inf	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	a1	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite106.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

825×	`prod-diff_binary64`
629×	`log-prod_binary64`
291×	`fma-def_binary64`
242×	`pow1/3_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	281	36
2	3635	36

Stop Event

1×	node limit

Counts

3 → 150

Calls

Call 1

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

Outputs

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

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

778×	`distribute-rgt-in_binary64`
682×	`distribute-lft-out_binary64`
501×	`associate-+l+_binary64`
488×	`unswap-sqr_binary64`
369×	`associate-+r+_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	1336
1	112	1192
2	341	1152
3	1654	1132
4	5397	1123

Stop Event

1×	node limit

Counts

234 → 175

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

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

localize18.0ms (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)

series4.0ms (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)))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	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)))))))))

simplify113.0ms (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

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)))

localize8.0ms (0%)

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))

rewrite46.0ms (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))))))))

simplify6.0ms (0%)

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

localize13.0ms (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)

series7.0ms (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	@	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	@	0	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
0.0ms	th	@	inf	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))

rewrite65.0ms (0.4%)

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))))))))

simplify204.0ms (1.2%)

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)))

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 42 to 17 computations (59.5% saved)

series5.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite67.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	261	17
2	3622	17

Stop Event

1×	node limit

Counts

1 → 85

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a2 a2)) 1) (*.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (*.f64 a1 a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a2 a1) 2))) (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a2 a1) 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a2 a1) 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a2 a1) 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 a2 a1) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (hypot.f64 a2 a1) 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 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) (neg.f64 (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (*.f64 (sqrt.f64 2) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (*.f64 (neg.f64 (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (*.f64 (sqrt.f64 2) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) 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simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	829
1	106	761
2	286	757
3	1028	725
4	3924	712

Stop Event

1×	node limit

Counts

121 → 101

Calls

Call 1

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

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

eval185.0ms (1.1%)

Compiler: Compiled 9339 to 5518 computations (40.9% saved)

prune114.0ms (0.7%)

Pruning

31 alts after pruning (26 fresh and 5 done)

	Pruned	Kept	Total
New	523	19	542
Fresh	7	7	14
Picked	0	1	1
Done	3	4	7
Total	533	31	564

Error

Counts

564 → 31

Alt Table

Click to see full alt table

Status	Error	Program
	25.1b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	39.3b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	43.4b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
✓	28.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	27.4b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
	39.3b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	27.4b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
	40.7b	(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
	39.3b	(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
	48.1b	(sqrt.f64 (/.f64 (pow.f64 a2 4) 2))
	39.3b	(.f64 a1 (.f64 (pow.f64 2 -1/2) a1))
	44.8b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
▶	54.3b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	27.4b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	40.6b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
	40.6b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	40.6b	(.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) 1)
✓	28.1b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
▶	28.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
✓	39.3b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	27.4b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
▶	40.6b	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
	27.4b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
▶	47.1b	(-.f64 (+.f64 1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	28.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	0.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	39.3b	(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
	39.3b	(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
	39.3b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

Compiler

Compiled 670 to 524 computations (21.8% saved)

localize43.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 46 to 21 computations (54.3% saved)

series9.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	a2	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
1.0ms	th	@	0	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms	th	@	0	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
1.0ms	th	@	inf	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms	a1	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite82.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 85

Calls

Call 1

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

Outputs

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

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

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

133 → 108

Calls

Call 1

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

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

localize10.0ms (0.1%)

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)

series3.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite45.0ms (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	15
1	120	15
2	1316	15

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

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

simplify174.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

34 → 24

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))

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (*.f64 a1 a1) 2)
✓	0.2b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
✓	21.2b	(sqrt.f64 (/.f64 (*.f64 a1 a1) 2))

Compiler

Compiled 27 to 14 computations (48.1% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

663×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
605×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	149	22
2	1791	22

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

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

Outputs

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

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

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

simplify102.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-def_binary64`
606×	`fma-neg_binary64`
581×	`distribute-rgt-neg-in_binary64`
571×	`distribute-lft-neg-in_binary64`
359×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	280
1	27	280
2	62	280
3	121	280
4	349	280
5	1206	280
6	1938	280
7	3218	280
8	4660	280
9	5367	280
10	5903	280
11	6677	280

Stop Event

1×	node limit

Counts

109 → 82

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	2.6b	(-.f64 (+.f64 1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)

Compiler

Compiled 35 to 23 computations (34.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite65.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

982×	`pow1_binary64`
924×	`add-log-exp_binary64`
923×	`log1p-expm1-u_binary64`
923×	`expm1-log1p-u_binary64`
102×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	203	18
2	2815	18

Stop Event

1×	node limit

Counts

2 → 115

Calls

Call 1

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

Outputs

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

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

simplify113.0ms (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	216
1	11	216
2	20	216
3	37	216
4	83	216
5	266	216
6	1091	216
7	3478	216
8	4280	216
9	4465	216
10	4681	216
11	5028	216
12	5456	216
13	5935	216
14	6584	216
15	7273	216

Stop Event

1×	node limit

Counts

139 → 73

Calls

Call 1

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

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 15 computations (46.4% saved)

series4.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite50.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

813×	`pow1_binary64`
748×	`add-log-exp_binary64`
748×	`log1p-expm1-u_binary64`
748×	`expm1-log1p-u_binary64`
729×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	181	23
2	2100	23

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

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

Outputs

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

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

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1027×	`fma-def_binary64`
840×	`unswap-sqr_binary64`
820×	`distribute-lft-out_binary64`
488×	`distribute-rgt-in_binary64`
366×	`*-commutative_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	532
1	86	532
2	262	508
3	1306	490
4	3584	483
5	5097	483
6	5318	483
7	5606	483
8	5886	483
9	6206	483
10	7605	483

Stop Event

1×	node limit

Counts

62 → 36

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))
(*.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 (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) (.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)))

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

eval123.0ms (0.7%)

Compiler: Compiled 5967 to 3705 computations (37.9% saved)

prune79.0ms (0.5%)

Pruning

37 alts after pruning (29 fresh and 8 done)

	Pruned	Kept	Total
New	368	15	383
Fresh	7	14	21
Picked	0	1	1
Done	2	7	9
Total	377	37	414

Error

Counts

414 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	25.1b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	40.8b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	39.3b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	43.4b	(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
✓	28.1b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (cos.f64 th)))
	27.4b	(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
	39.3b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	25.1b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	0.5b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
	27.4b	(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
	39.3b	(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
	27.4b	(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	46.7b	(.f64 a2 (-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) a2)) 1))
	44.8b	(.f64 a2 (.f64 (/.f64 a2 (sqrt.f64 2)) (+.f64 1 (.f64 th (.f64 th -1/2)))))
	40.6b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	54.3b	(.f64 a1 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)))
	27.4b	(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
	40.6b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
	39.3b	(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
	44.4b	(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/2 (*.f64 th th)))))
	0.5b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
	54.2b	(.f64 a1 (/.f64 1 (sqrt.f64 (/.f64 2 (.f64 a1 a1)))))
	54.2b	(.f64 (sqrt.f64 1/2) (.f64 a1 (neg.f64 a1)))
	40.6b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	28.1b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
✓	28.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	40.6b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
✓	39.3b	(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
	39.3b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	27.4b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
✓	47.1b	(-.f64 (+.f64 1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)
	54.2b	(.f64 a1 (.f64 a1 (neg.f64 (sqrt.f64 1/2))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	28.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	39.3b	(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
	27.4b	(.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (cos.f64 th))
	39.3b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))

Compiler

Compiled 438 to 337 computations (23.1% saved)

regimes498.0ms (2.9%)

Counts

69 → 1

Calls

Call 1

Inputs
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (neg.f64 a1)))
(.f64 a1 (.f64 a1 (neg.f64 (sqrt.f64 1/2))))
(.f64 a1 (.f64 (pow.f64 2 -1/2) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(*.f64 a1 (/.f64 1 (/.f64 (sqrt.f64 2) a1)))
(.f64 a1 (.f64 a1 (/.f64 1 (sqrt.f64 2))))
(/.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 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 a2 (-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) a2)) 1))
(.f64 a1 (/.f64 1 (sqrt.f64 (/.f64 2 (.f64 a1 a1)))))
(*.f64 a1 (-.f64 (+.f64 1 (/.f64 a1 (sqrt.f64 2))) 1))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(-.f64 (+.f64 1 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)
(.f64 a1 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))))
(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (+.f64 1 (.f64 -1/2 (*.f64 th th)))))
(.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))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(*.f64 a1 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1))
(.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (cos.f64 th))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(/.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 a2 (sqrt.f64 2)) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 (pow.f64 2 -1/2) (cos.f64 th)))
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (fma.f64 a1 a1 (*.f64 a2 a2)))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1) 2)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a2 a1)) 2)
(sqrt.f64 (.f64 (.f64 (pow.f64 (cos.f64 th) 2) 1/2) (pow.f64 (hypot.f64 a1 a2) 4)))
(.f64 (pow.f64 (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) (fma.f64 a1 a1 (.f64 a2 a2)))

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

Calls

11 calls:

72.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
66.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
60.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
48.0ms	a1
44.0ms	(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)`
0.4b	1	`(*.f64 a2 a2)`

Compiler

Compiled 742 to 438 computations (41% saved)

regimes318.0ms (1.9%)

Counts

63 → 1

Calls

Call 1

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

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

Calls

10 calls:

40.0ms	th
38.0ms	a1
37.0ms	a2
32.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
31.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 628 to 373 computations (40.6% saved)

regimes267.0ms (1.6%)

Counts

62 → 1

Calls

Call 1

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

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

Calls

8 calls:

38.0ms	a1
38.0ms	th
37.0ms	a2
32.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
31.0ms	(cos.f64 th)

Results

Error	Segments	Branch
0.4b	1	`a1`
0.4b	1	`a2`
0.4b	1	`th`
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 a2 a2)`

Compiler

Compiled 605 to 359 computations (40.7% saved)

regimes233.0ms (1.4%)

Counts

51 → 1

Calls

Call 1

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

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

Calls

8 calls:

33.0ms	a2
33.0ms	a1
32.0ms	th
29.0ms	(cos.f64 th)
28.0ms	(/.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	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.5b	1	`(cos.f64 th)`
0.5b	1	`(*.f64 a1 a1)`
0.5b	1	`(*.f64 a2 a2)`

Compiler

Compiled 486 to 297 computations (38.9% saved)

regimes962.0ms (5.6%)

Counts

48 → 2

Calls

Call 1

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

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

Calls

9 calls:

167.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
163.0ms	th
144.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
116.0ms	a2
104.0ms	(cos.f64 th)

Results

Error	Segments	Branch
4.5b	2	`a1`
7.0b	2	`a2`
12.2b	4	`th`
9.1b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.1b	5	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.1b	5	`(cos.f64 th)`
8.7b	2	`(*.f64 a1 a1)`
8.9b	3	`(*.f64 a2 a2)`
8.9b	3	`(*.f64 a2 a2)`

Compiler

Compiled 452 to 288 computations (36.3% saved)

bsearch67.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
67.0ms	-5.054766357456002e-114	-3.667422576523695e-116

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes470.0ms (2.7%)

Counts

40 → 2

Calls

Call 1

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

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

Calls

6 calls:

146.0ms	th
117.0ms	a2
77.0ms	(cos.f64 th)
44.0ms	a1
44.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
4.5b	2	`a1`
7.0b	2	`a2`
12.2b	4	`th`
9.1b	5	`(cos.f64 th)`
8.7b	2	`(*.f64 a1 a1)`
8.9b	3	`(*.f64 a2 a2)`

Compiler

Compiled 358 to 234 computations (34.6% saved)

bsearch103.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
102.0ms	-5.054766357456002e-114	-3.667422576523695e-116

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes481.0ms (2.8%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

7 calls:

122.0ms	a2
105.0ms	th
76.0ms	(cos.f64 th)
56.0ms	(*.f64 a1 a1)
39.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
4.5b	2	`a1`
7.0b	2	`a2`
12.2b	4	`th`
9.1b	5	`(cos.f64 th)`
8.7b	2	`(*.f64 a1 a1)`
8.7b	2	`(*.f64 a1 a1)`
8.9b	3	`(*.f64 a2 a2)`

Compiler

Compiled 337 to 225 computations (33.2% saved)

bsearch126.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
125.0ms	-5.054766357456002e-114	-3.667422576523695e-116

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes350.0ms (2%)

Counts

36 → 3

Calls

Call 1

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

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

Calls

6 calls:

79.0ms	a1
74.0ms	th
73.0ms	a2
60.0ms	(cos.f64 th)
31.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
14.9b	2	`a1`
15.9b	2	`a2`
13.9b	3	`th`
14.1b	2	`(cos.f64 th)`
16.4b	2	`(*.f64 a1 a1)`
16.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 322 to 217 computations (32.6% saved)

bsearch100.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
57.0ms	0.898846679155726	2005589.2032433744
42.0ms	-9.005873630663595e-8	-6.450167000098774e-13

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes352.0ms (2.1%)

Counts

35 → 3

Calls

Call 1

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

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

Calls

6 calls:

95.0ms	a2
80.0ms	th
73.0ms	a1
30.0ms	(cos.f64 th)
29.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
14.9b	2	`a1`
15.9b	2	`a2`
13.9b	3	`th`
14.1b	2	`(cos.f64 th)`
16.4b	2	`(*.f64 a1 a1)`
16.7b	2	`(*.f64 a2 a2)`

Compiler

Compiled 313 to 212 computations (32.3% saved)

bsearch172.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
81.0ms	0.898846679155726	2005589.2032433744
90.0ms	-9.005873630663595e-8	-6.450167000098774e-13

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes216.0ms (1.3%)

Counts

34 → 1

Calls

Call 1

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

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

Calls

5 calls:

56.0ms	(*.f64 a2 a2)
45.0ms	a1
39.0ms	a2
35.0ms	th
21.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
25.1b	1	`a1`
25.1b	1	`a2`
25.1b	1	`th`
25.1b	1	`(*.f64 a1 a1)`
25.1b	1	`(*.f64 a2 a2)`

Compiler

Compiled 299 to 203 computations (32.1% saved)

regimes522.0ms (3.1%)

Counts

19 → 2

Calls

Call 1

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

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

Calls

7 calls:

145.0ms	th
101.0ms	a2
94.0ms	(*.f64 a2 a2)
61.0ms	(*.f64 a2 a2)
51.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
26.6b	2	`a1`
29.1b	2	`a2`
33.6b	7	`th`
28.4b	2	`(*.f64 a1 a1)`
28.4b	2	`(*.f64 a1 a1)`
30.0b	4	`(*.f64 a2 a2)`
30.0b	4	`(*.f64 a2 a2)`

Compiler

Compiled 168 to 112 computations (33.3% saved)

bsearch70.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
70.0ms	-6.574657707543116e-133	-2.210414974602086e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes122.0ms (0.7%)

Counts

9 → 2

Calls

Call 1

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

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

Calls

7 calls:

38.0ms	th
18.0ms	a2
18.0ms	(*.f64 a2 a2)
17.0ms	(*.f64 a2 a2)
12.0ms	a1

Results

Error	Segments	Branch
26.6b	2	`a1`
29.1b	2	`a2`
33.7b	7	`th`
28.4b	2	`(*.f64 a1 a1)`
28.4b	2	`(*.f64 a1 a1)`
30.0b	4	`(*.f64 a2 a2)`
30.0b	4	`(*.f64 a2 a2)`

Compiler

Compiled 93 to 62 computations (33.3% saved)

bsearch66.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
65.0ms	-6.574657707543116e-133	-2.210414974602086e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes89.0ms (0.5%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

6 calls:

33.0ms	th
16.0ms	(*.f64 a2 a2)
14.0ms	a2
11.0ms	a1
7.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
26.6b	2	`a1`
29.1b	2	`a2`
33.7b	7	`th`
28.4b	2	`(*.f64 a1 a1)`
28.4b	2	`(*.f64 a1 a1)`
30.0b	4	`(*.f64 a2 a2)`

Compiler

Compiled 69 to 47 computations (31.9% saved)

bsearch69.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
68.0ms	-6.574657707543116e-133	-2.210414974602086e-137

Compiler

Compiled 28 to 20 computations (28.6% saved)

regimes17.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.1%)

Threshold costs -0.1b (-0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Error	Segments	Branch
40.6b	1	`a1`
40.6b	1	`a2`
40.6b	1	`th`
40.6b	1	`(*.f64 a2 a2)`

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	393
1	81	393

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 th 16580794651889399808/18446744073709551616) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (if (<=.f64 th 16580794651889399808/18446744073709551616) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)

Outputs
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (cos.f64 th) (sqrt.f64 1/2)))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 (cos.f64 th) (.f64 (*.f64 a2 a2) (sqrt.f64 1/2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th)) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (cos.f64 th) (.f64 (.f64 a1 a1) (sqrt.f64 1/2))) (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(if (<=.f64 a1 -7007598745089859/1386334847060407429789207092071541851718218537687908287585239790307310653902812811519987203052069789048695605480701785914487078912) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 (cos.f64 th) a1))) (.f64 (cos.f64 th) (.f64 (.f64 a2 a2) (sqrt.f64 1/2))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (cos.f64 th)))) (if (<=.f64 th 16580794651889399808/18446744073709551616) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 (cos.f64 th) a1))) (if (<=.f64 th 8096091138617871/9007199254740992) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)) (.f64 (.f64 a1 a1) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (if (<=.f64 th 16580794651889399808/18446744073709551616) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(if (<=.f64 th -1701161431296213/18889465931478580854784) (.f64 (.f64 a1 a1) (.f64 (cos.f64 th) (sqrt.f64 1/2))) (if (<=.f64 th 8096091138617871/9007199254740992) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)) (.f64 (.f64 a1 a1) (*.f64 (cos.f64 th) (sqrt.f64 1/2)))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 1/2))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(if (<=.f64 a1 -4203402888672581/6393341031047152089869511126616404594173128996177860916959553453312761321102879990006386899074031556935325554936640763689877454191182408307282280448) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

Compiler

Compiled 303 to 211 computations (30.4% saved)

soundness0.0ms (0%)

end126.0ms (0.7%)

Remove: (sort a1 a2)
Compiler: Compiled 291 to 161 computations (44.7% saved)