Details

analyze523.0ms (3.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
0%	0%	99.9%	0.1%	0%	0%	0%	5
25%	25%	74.9%	0.1%	0%	0%	0%	6
25%	25%	74.9%	0.1%	0%	0%	0%	7
25%	25%	74.9%	0.1%	0%	0%	0%	8
25%	25%	74.9%	0.1%	0%	0%	0%	9
28.1%	25%	64%	0.1%	10.9%	0%	0%	10
36.4%	31.2%	54.6%	0.1%	14%	0%	0%	11
46.9%	39%	44.1%	0.1%	16.8%	0%	0%	12

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.0s (25.3%)

Results

1.1s	5449×	body	256	valid
1.0s	1887×	body	1024	valid
843.0ms	1602×	body	1024	infinite
361.0ms	787×	body	512	infinite
337.0ms	1556×	body	256	infinite
293.0ms	917×	body	512	valid
2.0ms	3×	body	2048	valid
1.0ms	1×	body	2048	infinite

Bogosity

preprocess18.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

180×	`fma-def`
140×	`*-commutative`
114×	`associate-/l*`
48×	`associate-r`
48×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
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 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 th th)) (.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (+.f64 (.f64 th th) (*.f64 a2 a2)))
(.f64 (/.f64 (cos.f64 a1) (sqrt.f64 2)) (fma.f64 th th (.f64 a2 a2)))
(.f64 (cos.f64 a1) (/.f64 (fma.f64 th th (.f64 a2 a2)) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 th th)))
(.f64 (/.f64 (cos.f64 a2) (sqrt.f64 2)) (fma.f64 th th (.f64 a1 a1)))
(.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)

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

60×	`fma-def`
50×	`*-commutative`
40×	`associate-/l*`
18×	`associate-/r/`
16×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	30	35
2	56	35
3	79	35
4	106	35
5	124	35
6	142	35
7	147	35
8	149	35

Stop Event

1×

saturated

Counts

1 → 4

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 59 to 29 computations (50.8% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	2	2	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	2	5

Error

0.6b

Counts

5 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.7b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 31 to 21 computations (32.3% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 41 to 16 computations (61% saved)

series11.0ms (0.1%)

Counts

3 → 64

Calls

18 calls:

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

rewrite82.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1078×	`associate-*r/`
856×	`associate-*l/`
790×	`associate-/r*`
596×	`associate-/l*`
430×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	280	61
2	3399	61

Stop Event

1×	node limit

Counts

3 → 173

Calls

Call 1

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

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

Outputs

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

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

simplify154.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1618×	`distribute-lft-in`
820×	`times-frac`
808×	`associate-l`
778×	`associate-r`
518×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	468	9771
1	1178	9311
2	5962	9311

Stop Event

1×	node limit

Counts

237 → 278

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 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)))
1
(+.f64 1 (*.f64 -1/2 (pow.f64 th 2)))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 th 4)) (.f64 -1/2 (pow.f64 th 2))))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 th 4)) (+.f64 (.f64 -1/720 (pow.f64 th 6)) (*.f64 -1/2 (pow.f64 th 2)))))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 (.f64 a1 a1) 1)) (.f64 (pow.f64 2 -1/2) (*.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))
(+.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))
(+.f64 (.f64 (.f64 (.f64 a1 a1) 1) (pow.f64 2 -1/2)) (.f64 (*.f64 a2 a2) (pow.f64 2 -1/2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) 1)
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 -1/2))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)))
(.f64 (hypot.f64 a1 a2) (.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 -1/2)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (hypot.f64 a1 a2))
(*.f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) 1) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (cbrt.f64 2)) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)
(pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) -1)
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
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(cbrt.f64 (pow.f64 (cos.f64 th) 3))
(expm1.f64 (log1p.f64 (cos.f64 th)))
(exp.f64 (log.f64 (cos.f64 th)))
(exp.f64 (*.f64 (log.f64 (cos.f64 th)) 1))
(log1p.f64 (expm1.f64 (cos.f64 th)))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (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 a2 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 a2 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 a2 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 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (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 a2 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 a2 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 a2 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 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (+.f64 (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 a1 a1 (*.f64 a2 a2)) (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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (/.f64 (*.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 (.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 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))))
(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (/.f64 (.f64 (.f64 1/24 (fma.f64 a1 a1 (.f64 a2 a2))) (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)))))))
(fma.f64 -1/720 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))))))
(+.f64 (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (/.f64 (.f64 (.f64 1/24 (fma.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 a2) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (+.f64 (fma.f64 -1/2 (.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)) (.f64 th th)) (/.f64 (.f64 (.f64 1/24 (fma.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 a2) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (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 a1 a1 (.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (.f64 a2 (.f64 a2 (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(+.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (.f64 a2 (.f64 a2 (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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 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 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
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1
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(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) -1) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (cos.f64 th))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 (cbrt.f64 2) (cos.f64 th))))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 1)
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (*.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2))
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 3)
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3) 1/3)
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 2))
(sqrt.f64 (pow.f64 (/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2)) 2))
(fabs.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) 3))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) (pow.f64 (cos.f64 th) 3)))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3)))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (cos.f64 th))) 1)
(cos.f64 th)
(*.f64 (cos.f64 th) 1)
(cos.f64 th)
(*.f64 1 (cos.f64 th))
(cos.f64 th)
(*.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (cos.f64 th)))
(cos.f64 th)
(*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (pow.f64 (cos.f64 th) 2)))
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 th) 2)) (cbrt.f64 (cos.f64 th)))
(*.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (pow.f64 (cos.f64 th) 2)))
(pow.f64 (cos.f64 th) 1)
(cos.f64 th)
(pow.f64 (sqrt.f64 (cos.f64 th)) 2)
(cos.f64 th)
(pow.f64 (cbrt.f64 (cos.f64 th)) 3)
(cos.f64 th)
(pow.f64 (pow.f64 (cos.f64 th) 3) 1/3)
(cos.f64 th)
(sqrt.f64 (pow.f64 (cos.f64 th) 2))
(fabs.f64 (cos.f64 th))
(log.f64 (exp.f64 (cos.f64 th)))
(cos.f64 th)
(log.f64 (+.f64 1 (expm1.f64 (cos.f64 th))))
(cos.f64 th)
(cbrt.f64 (pow.f64 (cos.f64 th) 3))
(cos.f64 th)
(expm1.f64 (log1p.f64 (cos.f64 th)))
(cos.f64 th)
(exp.f64 (log.f64 (cos.f64 th)))
(cos.f64 th)
(exp.f64 (*.f64 (log.f64 (cos.f64 th)) 1))
(cos.f64 th)
(log1p.f64 (expm1.f64 (cos.f64 th)))
(cos.f64 th)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 th)
✓	0.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series5.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite104.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1226×	`associate-/r*`
844×	`associate-/l*`
836×	`distribute-rgt-in`
794×	`distribute-lft-in`
310×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	299	48
2	4071	48

Stop Event

1×	node limit

Counts

2 → 205

Calls

Call 1

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

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

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simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1310×	`associate-/l*`
826×	`associate-/r*`
810×	`times-frac`
764×	`associate-r`
744×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	604	13879
1	1684	13845

Stop Event

1×	node limit

Counts

245 → 327

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)))))
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(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) -1) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (neg.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)
(pow.f64 (*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (hypot.f64 a1 a2)) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 2))
(log.f64 (pow.f64 (exp.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 3))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))

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)))
(+.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))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 th 2) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2))) (+.f64 (*.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (*.f64 th th) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (pow.f64 th 6) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (pow.f64 th 4) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 2)))))
(/.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 (/.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 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th)))) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(+.f64 (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (.f64 -1/720 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 1/24 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)) (sqrt.f64 2)))))))
(fma.f64 -1/720 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (+.f64 (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(fma.f64 -1/720 (/.f64 (pow.f64 th 6) (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (+.f64 (fma.f64 -1/2 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.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 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
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(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3)))
(cbrt.f64 (*.f64 (pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 3) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (log.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))) 1))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))))
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))
(fma.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
(fma.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))

eval244.0ms (1.5%)

Compiler: Compiled 13628 to 8043 computations (41% saved)

prune425.0ms (2.7%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	617	19	636
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	618	20	638

Error

Counts

638 → 20

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
	0.7b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	26.8b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	30.6b	(/.f64 (.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
	26.7b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	30.2b	(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
	0.8b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
▶	30.3b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	29.6b	(.f64 (/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	30.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
	26.7b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	26.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	0.7b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	1.2b	(.f64 (.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	30.2b	(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
▶	30.2b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	26.7b	(*.f64 (cos.f64 th) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
▶	0.7b	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	0.7b	(.f64 (cos.f64 th) (.f64 (hypot.f64 a1 a2) (*.f64 (hypot.f64 a1 a2) (pow.f64 2 -1/2))))

Compiler

Compiled 602 to 427 computations (29.1% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 41 to 20 computations (51.2% saved)

series26.0ms (0.2%)

Counts

3 → 76

Calls

21 calls:

Time	Variable		Point	Expression
6.0ms	a1	@	0	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
4.0ms	a2	@	0	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
2.0ms	a1	@	0	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))
2.0ms	a1	@	inf	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
1.0ms	th	@	0	(/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2))

rewrite91.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1258×	`associate-/r/`
930×	`swap-sqr`
866×	`associate-/l/`
482×	`distribute-lft-neg-in`
430×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	81
1	275	75
2	3661	75

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

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

Outputs

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

simplify128.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1320×	`associate-r`
1260×	`*-commutative`
1136×	`associate-/r*`
1110×	`associate-l`
1066×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	856	16990
1	2577	16732

Stop Event

1×	node limit

Counts

304 → 419

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4)))))
(+.f64 (.f64 -1 (.f64 (+.f64 (.f64 1/48 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/2 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))))))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (+.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))) (.f64 -1 (.f64 (+.f64 (.f64 -1/4 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 1/24 (*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))) (pow.f64 th 4))))))
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(*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 (cbrt.f64 (hypot.f64 a1 a2)) (/.f64 1 (hypot.f64 a1 a2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) 1) (.f64 (/.f64 (cbrt.f64 (hypot.f64 a1 a2)) (sqrt.f64 2)) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (/.f64 (cbrt.f64 (hypot.f64 a1 a2)) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(*.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th))) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (hypot.f64 a1 a2) -1) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (pow.f64 2 1/4)))
(.f64 (/.f64 (hypot.f64 a1 a2) (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) (neg.f64 (sqrt.f64 2))) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))
(.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) -1) (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 2)) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 2)) (.f64 (/.f64 (hypot.f64 a1 a2) 1) (cos.f64 th)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) 1) (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) 1) (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (sqrt.f64 2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (pow.f64 2 1/4)) (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (pow.f64 2 1/4)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (cbrt.f64 2)) (/.f64 (.f64 (cos.f64 th) (hypot.f64 a1 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (neg.f64 (sqrt.f64 2))) (.f64 (hypot.f64 a1 a2) (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) -1) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (hypot.f64 a1 a2) (.f64 (sqrt.f64 2) (/.f64 1 (hypot.f64 a1 a2)))) (cos.f64 th))
(.f64 (/.f64 (hypot.f64 a1 a2) (.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (hypot.f64 a1 a2) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (cos.f64 th))
(.f64 (/.f64 (hypot.f64 a1 a2) (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (hypot.f64 a1 a2)) (cos.f64 th)))) (sqrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))) (sqrt.f64 (hypot.f64 a1 a2)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2) (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (sqrt.f64 (hypot.f64 a1 a2)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2))) -1) (neg.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) 1)) (cos.f64 th))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 1 (hypot.f64 a1 a2))) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (.f64 (sqrt.f64 2) (/.f64 1 (hypot.f64 a1 a2)))) (cos.f64 th))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (hypot.f64 a1 a2)))) (neg.f64 (cos.f64 th)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (hypot.f64 a1 a2))) (cos.f64 th))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (hypot.f64 a1 a2)) (cos.f64 th)))) (sqrt.f64 (hypot.f64 a1 a2)))
(*.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) 1) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 a1 a2)) 2))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) 1) (sqrt.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (pow.f64 2 1/4)) (sqrt.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) 1) (cbrt.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (cbrt.f64 (hypot.f64 a1 a2)))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (*.f64 (cos.f64 th) (hypot.f64 a1 a2))))
(.f64 (/.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (hypot.f64 a1 a2)))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (cbrt.f64 (neg.f64 (hypot.f64 a1 a2))))
(pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 3)
(pow.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2)) -1)
(neg.f64 (neg.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(neg.f64 (.f64 (hypot.f64 a1 a2) (.f64 (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))
(neg.f64 (.f64 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(neg.f64 (.f64 1 (neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(neg.f64 (/.f64 (neg.f64 (hypot.f64 a1 a2)) (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2)))))
(sqrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 2))
(log.f64 (exp.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 3) (pow.f64 (/.f64 (sqrt.f64 2) (*.f64 (cos.f64 th) (hypot.f64 a1 a2))) 3)))
(expm1.f64 (log1p.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (log.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))) 1))
(log1p.f64 (expm1.f64 (*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(*.f64 (sqrt.f64 2) (/.f64 1 (cos.f64 th)))
(*.f64 (sqrt.f64 2) (neg.f64 (/.f64 -1 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(*.f64 1 (/.f64 (sqrt.f64 2) (cos.f64 th)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (neg.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 (cos.f64 th))))
(*.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 2))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 -1 (cos.f64 th)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))))
(*.f64 (/.f64 1 (sqrt.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (cos.f64 th))))
(*.f64 -1 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 -1 (cos.f64 th)) (neg.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (cos.f64 th)))
(*.f64 (/.f64 (pow.f64 2 1/4) (cos.f64 th)) (pow.f64 2 1/4))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 (cos.f64 th))) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(*.f64 (/.f64 1 (/.f64 (cos.f64 th) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (cbrt.f64 2) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(*.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 1)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3) 1/3)
(pow.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1)
(neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th))) 1))
(sqrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) 3))
(cbrt.f64 (/.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 (cos.f64 th) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))

Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(+.f64 (.f64 1/2 (.f64 (.f64 (sqrt.f64 2) (pow.f64 th 2)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (.f64 th th) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (.f64 th th))) (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
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(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))
(/.f64 (sqrt.f64 2) (cos.f64 th))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (sqrt.f64 2) (cos.f64 th))

localize11.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 31 to 12 computations (61.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1010×	`associate-*r/`
990×	`*-commutative`
778×	`associate-/r*`
752×	`associate-*l/`
616×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	233	23
2	3053	23

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

Outputs

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

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1186×	`associate-*r/`
872×	`associate-/l*`
778×	`associate-+r-`
756×	`associate-+l-`
752×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2637
1	401	2549
2	1536	2479
3	6966	2479

Stop Event

1×	node limit

Counts

75 → 78

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)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))
(+.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))) 1)
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)))
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(*.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)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)))
(*.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))))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) 1))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)))
(*.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)))
(*.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)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)))
(*.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))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))
(.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.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))))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 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 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(+.f64 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(+.f64 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(+.f64 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(/.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 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(/.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 (/.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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 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 (/.f64 a2 (sqrt.f64 2)) a2))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)) (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (pow.f64 2 -1/2) (.f64 a1 a1)) (.f64 (pow.f64 2 -1/2) (.f64 a2 a2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)) (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a1 a1) (pow.f64 2 -1/2)) (.f64 (.f64 a2 a2) (pow.f64 2 -1/2)))
(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (pow.f64 2 -1/2) (fma.f64 a1 a1 (.f64 a2 a2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))) 1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 -1/2))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 1 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (hypot.f64 a2 a1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.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)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)))
(*.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))))
(*.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)))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2)))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (/.f64 -1 (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (/.f64 (hypot.f64 a2 a1) 1))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) 1))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (pow.f64 2 1/4)) (/.f64 1 (pow.f64 2 1/4)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (/.f64 1 (cbrt.f64 2)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) 1) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 2)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.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)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.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)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (pow.f64 2 1/4)) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (pow.f64 2 1/4)))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(*.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))))
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (cbrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2) (sqrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2))) (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(*.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (pow.f64 (hypot.f64 a2 a1) 2))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.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))))
(.f64 (/.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a2 4) (+.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (.f64 (+.f64 (pow.f64 a1 4) (+.f64 (pow.f64 (.f64 a1 a2) 2) (pow.f64 a2 4))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (*.f64 (sqrt.f64 2) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(.f64 (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 2)) (/.f64 (+.f64 (pow.f64 (.f64 a1 a2) 2) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a2 a1) 2)))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (-.f64 (pow.f64 a2 8) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (+.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2)))
(.f64 1 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 2)) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) 3))) (-.f64 (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)) (sqrt.f64 2))) (+.f64 (pow.f64 a2 8) (-.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (sqrt.f64 2) (+.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)))) (+.f64 (pow.f64 a2 8) (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (pow.f64 a2 4)))))
(.f64 (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (.f64 (sqrt.f64 2) (+.f64 (pow.f64 (.f64 a2 a2) 6) (pow.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) 3)))) (fma.f64 (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)) (-.f64 (pow.f64 a1 4) (+.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))) (pow.f64 a2 8)))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (/.f64 (hypot.f64 a2 a1) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))) 3)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3) 1/3)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a2 a1) 2)) -1)
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(neg.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (neg.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2) 2))
(sqrt.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 4) 2))
(log.f64 (exp.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2)) 3))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a2 a1) 2) (sqrt.f64 2))

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 29 to 19 computations (34.5% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

12 calls:

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

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1522×	`associate-*l/`
1416×	`associate-/l*`
1108×	`*-commutative`
602×	`associate-/r/`
268×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	55
1	229	55
2	2975	55

Stop Event

1×	node limit

Counts

3 → 209

Calls

Call 1

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

Outputs

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

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1064×	`distribute-rgt-in`
1048×	`distribute-lft-in`
1014×	`associate-/l*`
886×	`times-frac`
628×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	477	6643
1	1329	6409
2	6091	6409

Stop Event

1×	node limit

Counts

245 → 276

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 (/.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 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) a2))) 1)
(*.f64 (sqrt.f64 2) (/.f64 1 a2))
(*.f64 (sqrt.f64 2) (neg.f64 (neg.f64 (/.f64 1 a2))))
(*.f64 (/.f64 (sqrt.f64 2) a2) 1)
(*.f64 1 (/.f64 (sqrt.f64 2) a2))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (/.f64 1 a2)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 a2)))
(.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cbrt.f64 (/.f64 2 (.f64 a2 a2))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)))
(.f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(.f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2))) (neg.f64 (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))))
(*.f64 (/.f64 1 a2) (sqrt.f64 2))
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (/.f64 1 a2)))
(*.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (neg.f64 a2)))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))))
(.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))))
(.f64 (.f64 (pow.f64 2 1/4) (/.f64 1 a2)) (pow.f64 2 1/4))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (/.f64 1 a2)) (cbrt.f64 2))
(*.f64 (/.f64 1 (sqrt.f64 a2)) (/.f64 (sqrt.f64 2) (sqrt.f64 a2)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 a2)))
(*.f64 (/.f64 (sqrt.f64 2) 1) (/.f64 1 a2))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 a2)) (/.f64 1 (sqrt.f64 a2)))
(*.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 a2)) (/.f64 1 (pow.f64 (cbrt.f64 a2) 2)))
(*.f64 -1 (/.f64 (sqrt.f64 2) (neg.f64 a2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))
(.f64 (neg.f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (neg.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2))))
(*.f64 (/.f64 1 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2))) 1) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(*.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) a2))
(*.f64 (/.f64 (pow.f64 2 1/4) a2) (pow.f64 2 1/4))
(*.f64 (/.f64 (pow.f64 2 1/4) a2) (/.f64 (pow.f64 2 1/4) 1))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 a2)))
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 a2)) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a2) 2)))
(*.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) a2))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2) (/.f64 (cbrt.f64 2) 1))
(*.f64 (/.f64 (cbrt.f64 2) (sqrt.f64 a2)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 a2)))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (sqrt.f64 a2)) (/.f64 (cbrt.f64 2) (sqrt.f64 a2)))
(*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(*.f64 (/.f64 (cbrt.f64 2) a2) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 1 (/.f64 a2 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (.f64 a2 a2))))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(pow.f64 (/.f64 (sqrt.f64 2) a2) 1)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) 2)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 2) a2) 3) 1/3)
(pow.f64 (/.f64 a2 (sqrt.f64 2)) -1)
(neg.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)))
(neg.f64 (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)) 1))
(sqrt.f64 (/.f64 2 (*.f64 a2 a2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 2) a2)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) a2))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 2) a2) 3))
(cbrt.f64 (/.f64 2 (/.f64 (pow.f64 a2 3) (sqrt.f64 2))))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) a2)))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 2) a2)))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) a2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(.f64 1 (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) a2)))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 2))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 2) (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(*.f64 (cbrt.f64 a2) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) a2)))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
(*.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 a2 1))
(*.f64 (neg.f64 a2) (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) a2)) (sqrt.f64 a2))
(*.f64 (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) a2)) (/.f64 (sqrt.f64 a2) 1))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (sqrt.f64 2) a2)) (cbrt.f64 a2))
(*.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 a2 1) a2))
(*.f64 (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)) (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) a2))))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (.f64 (/.f64 a2 1) a2) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 1 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 a2 (neg.f64 a2)))
(.f64 (/.f64 (sqrt.f64 a2) (sqrt.f64 2)) (.f64 (/.f64 a2 1) (sqrt.f64 a2)))
(.f64 (.f64 (/.f64 a2 1) (sqrt.f64 a2)) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 2) a2)))
(.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))))
(.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 (sqrt.f64 a2) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)) (.f64 (/.f64 a2 1) (cbrt.f64 a2)))
(.f64 (.f64 (/.f64 a2 1) (cbrt.f64 a2)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (.f64 (cbrt.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 a2) (/.f64 a2 (sqrt.f64 2))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (.f64 (cbrt.f64 a2) (/.f64 a2 (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 (cbrt.f64 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))
(*.f64 (/.f64 (cbrt.f64 a2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(*.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))) (neg.f64 a2))
(*.f64 (/.f64 (neg.f64 a2) (sqrt.f64 2)) (neg.f64 a2))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a2) 2))) (cbrt.f64 a2))
(*.f64 (/.f64 a2 -1) (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 a2 (pow.f64 (cbrt.f64 a2) 2)))) (cbrt.f64 a2))
(*.f64 (/.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 1 (sqrt.f64 a2))) (sqrt.f64 a2))
(*.f64 (/.f64 (/.f64 a2 (sqrt.f64 2)) (/.f64 1 (pow.f64 (cbrt.f64 a2) 2))) (cbrt.f64 a2))
(*.f64 (/.f64 (/.f64 a2 (sqrt.f64 2)) -1) (neg.f64 a2))
(*.f64 (/.f64 (neg.f64 a2) -1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 a2 1) 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 (/.f64 a2 1) (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (/.f64 (/.f64 a2 1) (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 a2 1) (neg.f64 (sqrt.f64 2))) (neg.f64 a2))
(*.f64 (/.f64 (/.f64 a2 1) (/.f64 (sqrt.f64 2) 1)) a2)
(*.f64 (/.f64 (/.f64 a2 1) (/.f64 (sqrt.f64 2) (sqrt.f64 a2))) (sqrt.f64 a2))
(*.f64 (/.f64 (/.f64 a2 1) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a2) 2))) (cbrt.f64 a2))
(*.f64 (/.f64 (/.f64 a2 1) -1) (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) 1) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (/.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 a2)))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) 1) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 a2))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 a2)))
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
(neg.f64 (/.f64 (*.f64 a2 (neg.f64 a2)) (sqrt.f64 2)))
(neg.f64 (*.f64 a2 (/.f64 a2 (neg.f64 (sqrt.f64 2)))))
(neg.f64 (.f64 (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2)) 1))
(neg.f64 (.f64 1 (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2))))
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) 1)
(/.f64 a2 (/.f64 (/.f64 (sqrt.f64 2) a2) (cos.f64 th)))
(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (.f64 a2 (cos.f64 th)) a2)))
(/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cos.f64 th)))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (sqrt.f64 (cos.f64 th))))
(/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) a2) (*.f64 a2 (sqrt.f64 (cos.f64 th)))))
(/.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cbrt.f64 (cos.f64 th))))
(/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) a2) (*.f64 a2 (cbrt.f64 (cos.f64 th)))))
(/.f64 (*.f64 a2 (cos.f64 th)) (/.f64 (sqrt.f64 2) a2))
(/.f64 (neg.f64 a2) (/.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2)) (cos.f64 th)))
(/.f64 (sqrt.f64 (.f64 a2 (cos.f64 th))) (/.f64 (/.f64 (sqrt.f64 2) a2) (sqrt.f64 (.f64 a2 (cos.f64 th)))))
(/.f64 (.f64 (cbrt.f64 (.f64 a2 (cos.f64 th))) (cbrt.f64 (.f64 a2 (cos.f64 th)))) (/.f64 (/.f64 (sqrt.f64 2) a2) (cbrt.f64 (.f64 a2 (cos.f64 th)))))
(/.f64 (.f64 (cos.f64 th) (sqrt.f64 a2)) (/.f64 (sqrt.f64 2) (.f64 a2 (sqrt.f64 a2))))
(/.f64 (.f64 (cos.f64 th) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (sqrt.f64 2) (.f64 a2 (cbrt.f64 a2))))
(/.f64 (*.f64 a2 (neg.f64 (cos.f64 th))) (/.f64 (sqrt.f64 2) (neg.f64 a2)))
(/.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 1 a2))
(/.f64 (/.f64 a2 (/.f64 1 (cos.f64 th))) (/.f64 (sqrt.f64 2) a2))
(/.f64 (/.f64 a2 (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (sqrt.f64 a2) (sqrt.f64 (cos.f64 th))) (/.f64 (/.f64 (sqrt.f64 2) a2) (.f64 (sqrt.f64 a2) (sqrt.f64 (cos.f64 th)))))
(/.f64 (.f64 (.f64 a2 a2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 1) (cos.f64 th)) (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th)) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cos.f64 th)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 -1 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2))))
(/.f64 (.f64 (.f64 a2 (neg.f64 (cos.f64 th))) 1) (/.f64 (sqrt.f64 2) (neg.f64 a2)))
(/.f64 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1) (/.f64 1 a2))
(/.f64 (*.f64 (/.f64 a2 (/.f64 1 (cos.f64 th))) 1) (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) 1) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (sqrt.f64 (.f64 a2 (cos.f64 th))) (*.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 1 (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))))
(/.f64 (.f64 (sqrt.f64 a2) (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (sqrt.f64 (neg.f64 a2)) (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(/.f64 (.f64 (cbrt.f64 (.f64 a2 (cos.f64 th))) (pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (sqrt.f64 a2) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 a2)))
(/.f64 (.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 2) (cbrt.f64 a2)))
(/.f64 (.f64 (neg.f64 a2) (.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (/.f64 a2 1) (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 (cos.f64 th))) (/.f64 1 a2))
(/.f64 (.f64 (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)) (.f64 a2 (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (*.f64 a2 (cos.f64 th))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (.f64 a2 (cos.f64 th))) (pow.f64 2 1/4))
(/.f64 (.f64 (/.f64 a2 (cbrt.f64 2)) (.f64 a2 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (.f64 (/.f64 a2 1) a2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))) (cbrt.f64 (/.f64 2 (.f64 a2 a2))))
(pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(pow.f64 (*.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3) 1/3)
(neg.f64 (.f64 (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2)) (cos.f64 th)))
(neg.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2))))
(neg.f64 (*.f64 (/.f64 a2 (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))) a2))
(neg.f64 (.f64 (/.f64 (cos.f64 th) 1) (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2))))
(neg.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) (pow.f64 (cos.f64 th) 3)))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 (*.f64 a2 a2) th) th))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 (.f64 a2 a2) 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 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) (.f64 a2 a2))) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (pow.f64 th 4) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (/.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) (*.f64 a2 a2))) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
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(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 1) (cos.f64 th)) (/.f64 (sqrt.f64 2) a2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th)) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cos.f64 th)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th)))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th))
(/.f64 (.f64 -1 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (.f64 a2 (neg.f64 (cos.f64 th))) 1) (/.f64 (sqrt.f64 2) (neg.f64 a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) 1) (/.f64 1 a2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 (/.f64 1 (cos.f64 th))) 1) (/.f64 (sqrt.f64 2) a2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 a2 (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th))) 1) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) 1) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th)))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th))
(/.f64 (.f64 (sqrt.f64 (.f64 a2 (cos.f64 th))) (*.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (.f64 (.f64 (sqrt.f64 (*.f64 a2 (cos.f64 th))) (/.f64 a2 (pow.f64 2 1/4))) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (sqrt.f64 (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th)))))
(/.f64 (.f64 1 (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))))
(/.f64 (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2))))
(/.f64 (.f64 a2 (cos.f64 th)) (.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))) (pow.f64 2 1/4)))
(/.f64 (.f64 (sqrt.f64 a2) (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.f64 a2 (cos.f64 th)) (pow.f64 2 1/4))))
(/.f64 (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (sqrt.f64 (neg.f64 a2)) (.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(/.f64 (.f64 (sqrt.f64 (neg.f64 a2)) (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 2 1/4))) (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(/.f64 (sqrt.f64 (neg.f64 a2)) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (neg.f64 a2))) (*.f64 (cos.f64 th) (/.f64 a2 (pow.f64 2 1/4)))))
(/.f64 (.f64 (cbrt.f64 (.f64 a2 (cos.f64 th))) (pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 2)) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (cbrt.f64 (.f64 a2 (cos.f64 th))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (pow.f64 (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th))))) 2)))
(.f64 (/.f64 (cbrt.f64 (.f64 a2 (cos.f64 th))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (pow.f64 (cbrt.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))) 2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (sqrt.f64 a2) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 2) (sqrt.f64 a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 a2 (cos.f64 th))) (/.f64 (sqrt.f64 2) (cbrt.f64 a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (neg.f64 a2) (.f64 a2 (cos.f64 th))) (neg.f64 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 a2 1) (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 (cos.f64 th))) (/.f64 1 a2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)) (.f64 a2 (cos.f64 th))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (sqrt.f64 a2) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.f64 a2 (cos.f64 th)) (pow.f64 2 1/4))))
(/.f64 (/.f64 (sqrt.f64 a2) (pow.f64 2 1/4)) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (*.f64 a2 (cos.f64 th))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th)))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th))
(/.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (.f64 a2 (cos.f64 th))) (pow.f64 2 1/4))
(/.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 (pow.f64 2 1/4) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (pow.f64 2 1/2))
(/.f64 (.f64 (/.f64 a2 (cbrt.f64 2)) (.f64 a2 (cos.f64 th))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) a2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (.f64 a2 (cos.f64 th)) (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 (/.f64 a2 1) a2)) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (/.f64 a2 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (/.f64 a2 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))) (cbrt.f64 (/.f64 2 (.f64 a2 a2))))
(/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (*.f64 a2 a2)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cos.f64 th)))
(.f64 (/.f64 (/.f64 a2 (cbrt.f64 (/.f64 2 (.f64 a2 a2)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cos.f64 th))
(pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(pow.f64 (*.f64 (/.f64 a2 (pow.f64 2 1/4)) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 3)
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3) 1/3)
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(neg.f64 (.f64 (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2)) (cos.f64 th)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(neg.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(neg.f64 (*.f64 (/.f64 a2 (/.f64 (neg.f64 (sqrt.f64 2)) (cos.f64 th))) a2))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(neg.f64 (.f64 (/.f64 (cos.f64 th) 1) (/.f64 (.f64 a2 (neg.f64 a2)) (sqrt.f64 2))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(neg.f64 (/.f64 (*.f64 a2 (cos.f64 th)) (/.f64 (sqrt.f64 2) (neg.f64 a2))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 2))
(sqrt.f64 (pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))) 2))
(fabs.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(cbrt.f64 (.f64 (pow.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) (pow.f64 (cos.f64 th) 3)))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 28 to 15 computations (46.4% saved)

series1.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite74.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1802×	`associate-/l*`
1502×	`associate-*l/`
1098×	`*-commutative`
590×	`associate-/r/`
398×	`associate-/l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	230	44
2	3100	44

Stop Event

1×	node limit

Counts

2 → 151

Calls

Call 1

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

Outputs

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

simplify130.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1398×	`unswap-sqr`
698×	`distribute-rgt-in`
682×	`distribute-lft-in`
580×	`distribute-lft-neg-in`
576×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	365	5949
1	1064	5781
2	3918	5781

Stop Event

1×	node limit

Counts

187 → 228

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 4)) (sqrt.f64 2))) (+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))) (.f64 -1/720 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 6)) (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)))) 1)
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)) 1)
(.f64 1 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))
(*.f64 (/.f64 (pow.f64 2 1/4) a2) (/.f64 (pow.f64 2 1/4) a2))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) (pow.f64 a2 -2)))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a2 4))))
(.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a2 -2)))
(*.f64 (/.f64 (sqrt.f64 2) a2) (/.f64 1 a2))
(*.f64 (pow.f64 a2 -2) (sqrt.f64 2))
(*.f64 (neg.f64 (sqrt.f64 2)) (neg.f64 (pow.f64 a2 -2)))
(.f64 (neg.f64 (sqrt.f64 2)) (/.f64 1 (.f64 a2 (neg.f64 a2))))
(.f64 (.f64 (pow.f64 2 1/4) (pow.f64 a2 -2)) (pow.f64 2 1/4))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (pow.f64 a2 -2)) (cbrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 2) 1) (pow.f64 a2 -2))
(*.f64 (/.f64 1 a2) (/.f64 (sqrt.f64 2) a2))
(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 a2 4))) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)))
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 1 (cbrt.f64 (pow.f64 a2 4))))
(.f64 -1 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2))))
(*.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a2)) (neg.f64 (/.f64 (pow.f64 2 1/4) a2)))
(.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (neg.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))))
(.f64 (/.f64 1 (.f64 a2 (neg.f64 a2))) (neg.f64 (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 2 1/4) 1) (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)) (pow.f64 2 1/4))
(.f64 (/.f64 (pow.f64 2 1/4) (.f64 a2 a2)) (/.f64 (pow.f64 2 1/4) 1))
(*.f64 (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a2 4))) (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a2) 2)))
(*.f64 (/.f64 (pow.f64 2 1/4) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (pow.f64 2 1/4) (cbrt.f64 (pow.f64 a2 4))))
(*.f64 (/.f64 (cbrt.f64 2) a2) (/.f64 (cbrt.f64 (sqrt.f64 2)) a2))
(*.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2) (/.f64 (cbrt.f64 2) a2))
(.f64 (/.f64 (cbrt.f64 2) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a2 a2)))
(.f64 (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a2 a2)) (/.f64 (cbrt.f64 2) 1))
(.f64 (/.f64 (cbrt.f64 2) (cbrt.f64 (pow.f64 a2 4))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(.f64 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) 1) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(.f64 (/.f64 (cbrt.f64 2) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (/.f64 1 (/.f64 (.f64 a2 a2) (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(.f64 (neg.f64 (sqrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2))))) (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))))
(.f64 (neg.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))) (cbrt.f64 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))))) (cbrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))))
(*.f64 (neg.f64 (neg.f64 (/.f64 (pow.f64 2 1/4) a2))) (/.f64 (pow.f64 2 1/4) a2))
(.f64 (neg.f64 (neg.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)) 1)
(pow.f64 (/.f64 (pow.f64 2 1/4) a2) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)) 3) 1/3)
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) -1)
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2))))
(sqrt.f64 (/.f64 2 (pow.f64 a2 4)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 a2 -2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)))))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)) 3))
(cbrt.f64 (/.f64 2 (/.f64 (pow.f64 (*.f64 a2 a2) 3) (sqrt.f64 2))))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))) 1)
(*.f64 a2 (/.f64 a2 (/.f64 (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 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(.f64 1 (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))))
(.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4))) (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (cbrt.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (cos.f64 th))
(.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (/.f64 (cos.f64 th) 1))
(.f64 (neg.f64 (cos.f64 th)) (.f64 (neg.f64 (/.f64 a2 (sqrt.f64 2))) a2))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (cos.f64 th) (sqrt.f64 2))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (.f64 (sqrt.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))
(.f64 (/.f64 (cos.f64 th) 1) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cos.f64 th) (cbrt.f64 2)) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2)))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(*.f64 (/.f64 1 (sqrt.f64 2)) (/.f64 (cos.f64 th) (pow.f64 a2 -2)))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (/.f64 (cos.f64 th) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))))
(*.f64 (/.f64 (cos.f64 th) (pow.f64 a2 -2)) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))) (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))))
(.f64 (/.f64 a2 (sqrt.f64 2)) (.f64 a2 (cos.f64 th)))
(.f64 (/.f64 a2 (pow.f64 2 1/4)) (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) a2)
(.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (.f64 a2 (neg.f64 a2)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 (cos.f64 th) (*.f64 a2 (neg.f64 a2))))
(*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a2 -2)))
(*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 a2 -2)) (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) 1) (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 a2)) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 a2)) (/.f64 (sqrt.f64 (cos.f64 th)) 1))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))) (/.f64 (sqrt.f64 (cos.f64 th)) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)) (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a2 -2)))
(*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 a2 -2)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (sqrt.f64 2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1) (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 a2)))
(.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (sqrt.f64 2)) (*.f64 a2 a2)) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) 1))
(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a2) (*.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a2))
(.f64 (.f64 (/.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a2) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 2 1/4)) a2))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (.f64 (neg.f64 (/.f64 a2 (sqrt.f64 2))) a2) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) (cbrt.f64 (cos.f64 th)))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4)))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a2 (sqrt.f64 a2)))) (sqrt.f64 a2))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (/.f64 (sqrt.f64 2) a2) (pow.f64 (cbrt.f64 a2) 2))) (cbrt.f64 a2))
(.f64 (/.f64 (cos.f64 th) -1) (.f64 (neg.f64 (/.f64 a2 (sqrt.f64 2))) a2))
(*.f64 (/.f64 (cos.f64 th) (neg.f64 (/.f64 (sqrt.f64 2) a2))) (neg.f64 a2))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (pow.f64 a2 -2)))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (.f64 a2 a2))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) 1) (/.f64 a2 (/.f64 1 a2)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 a2)) a2)
(*.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 1 (cbrt.f64 (pow.f64 a2 4)))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) -1) (.f64 a2 (neg.f64 a2)))
(.f64 (/.f64 (neg.f64 (cos.f64 th)) -1) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (/.f64 (neg.f64 (cos.f64 th)) (neg.f64 (/.f64 (sqrt.f64 2) a2))) a2)
(.f64 (/.f64 (neg.f64 (cos.f64 th)) (sqrt.f64 2)) (.f64 a2 (neg.f64 a2)))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) 1) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (cbrt.f64 2)) (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) a2)) a2)
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (sqrt.f64 2))) (.f64 a2 (neg.f64 a2)))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) 1)) (.f64 a2 a2))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4)))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (sqrt.f64 2) (.f64 a2 (sqrt.f64 a2)))) (sqrt.f64 a2))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (/.f64 (/.f64 (sqrt.f64 2) a2) (pow.f64 (cbrt.f64 a2) 2))) (cbrt.f64 a2))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) -1) (.f64 (neg.f64 (/.f64 a2 (sqrt.f64 2))) a2))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (/.f64 (sqrt.f64 2) a2))) (neg.f64 a2))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) 1) (sqrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (sqrt.f64 a2))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 a2 (neg.f64 a2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) 1) (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (cbrt.f64 a2) 2))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cbrt.f64 a2))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 a2 (neg.f64 a2))))
(pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3) 1/3)
(pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a2 -2)) -1)
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 (neg.f64 a2))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))

Outputs
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (pow.f64 a2 2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th))))
(fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 -1/2 (.f64 (.f64 a2 th) (.f64 a2 th))) (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 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)))))
(fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (pow.f64 th 4)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (/.f64 (.f64 -1/2 (.f64 (.f64 a2 th) (*.f64 a2 th))) (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))))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) (.f64 a2 a2))) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a2 a2)) (sqrt.f64 2))))))
(fma.f64 1/24 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (pow.f64 th 4)) (fma.f64 a2 (/.f64 a2 (sqrt.f64 2)) (fma.f64 -1/2 (.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (.f64 th th)) (/.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) (.f64 a2 a2))) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)))) 1)
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)) 1)
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(.f64 1 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))
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(.f64 (cbrt.f64 a2) (.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) 1) -1) (.f64 (neg.f64 (/.f64 a2 (sqrt.f64 2))) a2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(*.f64 (/.f64 (/.f64 (cos.f64 th) 1) (neg.f64 (/.f64 (sqrt.f64 2) a2))) (neg.f64 a2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) 1) (sqrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (sqrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (sqrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) (sqrt.f64 (/.f64 (sqrt.f64 2) a2))) (sqrt.f64 a2))
(/.f64 (.f64 (/.f64 (.f64 a2 (cos.f64 th)) (pow.f64 2 1/4)) (sqrt.f64 a2)) (sqrt.f64 (/.f64 (sqrt.f64 2) a2)))
(/.f64 (*.f64 a2 (/.f64 (cos.f64 th) (pow.f64 2 1/4))) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) a2)) (sqrt.f64 a2)))
(.f64 (/.f64 (.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) a2) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (*.f64 a2 (neg.f64 a2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (pow.f64 2 1/4)) (/.f64 (sqrt.f64 (neg.f64 (sqrt.f64 2))) a2)) (sqrt.f64 (.f64 a2 (neg.f64 a2))))
(.f64 (/.f64 a2 (/.f64 (sqrt.f64 (neg.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))) (sqrt.f64 (neg.f64 (.f64 a2 a2))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) 1) (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 (cos.f64 th) (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (sqrt.f64 2))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) (cbrt.f64 (sqrt.f64 2)))))
(*.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2))) (cbrt.f64 a2))
(.f64 (cbrt.f64 a2) (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (/.f64 (sqrt.f64 2) a2)) (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))))
(.f64 (cbrt.f64 a2) (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) (cbrt.f64 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (/.f64 (/.f64 (cos.f64 th) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (.f64 a2 (neg.f64 a2))))
(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (/.f64 2 (pow.f64 a2 4))))) (cbrt.f64 (*.f64 a2 (neg.f64 a2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (cbrt.f64 (neg.f64 (.f64 a2 a2)))) (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (*.f64 a2 a2))))
(pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(pow.f64 (*.f64 a2 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))) 3)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3) 1/3)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(pow.f64 (*.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 a2 -2)) -1)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(neg.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 (neg.f64 a2))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))
(sqrt.f64 (*.f64 (pow.f64 a2 4) (/.f64 (pow.f64 (cos.f64 th) 2) 2)))
(sqrt.f64 (/.f64 (pow.f64 (cos.f64 th) 2) (/.f64 2 (pow.f64 a2 4))))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 3))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(*.f64 a2 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)))

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 th)
✓	0.4b	(.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)

series6.0ms (0%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
2.0ms	a2	@	inf	(.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)))
0.0ms	th	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	th	@	inf	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
0.0ms	a2	@	0	(.f64 (cos.f64 th) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`associate-*r/`
864×	`distribute-rgt-in`
818×	`distribute-lft-in`
700×	`associate-*l/`
328×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	320	56
2	4148	56

Stop Event

1×	node limit

Counts

2 → 156

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))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 1) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1)) (*.f64 1 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1) 1) (*.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 1) 1))))) (#(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 /.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (+.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 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2)) (+.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 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))) (-.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 3)) (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (*.f64 a1 a1) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 1/2) (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 (sqrt.f64 1/2) (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 (*.f64 1 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (sqrt.f64 1/2) (+.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 1 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2))) (-.f64 (*.f64 a2 a2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2))) (+.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 1 (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))) (-.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (+.f64 (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 3))) (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) (-.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (hypot.f64 a2 a1)) (sqrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 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simplify144.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1498×	`distribute-lft-in`
1466×	`distribute-rgt-in`
1082×	`associate-/l*`
756×	`associate-r`
754×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	11132
1	1124	10306
2	5017	10306

Stop Event

1×	node limit

Counts

216 → 246

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)))
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(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))
(+.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2)) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (cos.f64 th)) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th)) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (cos.f64 th)))
(+.f64 (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(+.f64 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(+.f64 (.f64 (cos.f64 th) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)) (.f64 (cos.f64 th) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1)))
(+.f64 (.f64 1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))) (.f64 1 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))))
(+.f64 (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2))) (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1))))
(+.f64 (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1))) (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2))))
(+.f64 (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (cos.f64 th))) (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th))))
(+.f64 (.f64 1 (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 1 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(+.f64 (.f64 1 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 1 (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th)))))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (.f64 a2 a2)) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (.f64 a1 a1)))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (.f64 a1 a1)) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1) (cos.f64 th)) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1) (cos.f64 th)))
(+.f64 (.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1) (.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 1))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2)) 1) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1)) 1))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a1 a1)) 1) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (.f64 a2 a2)) 1))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (cos.f64 th)) 1) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (cos.f64 th)) 1))
(+.f64 (.f64 (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (.f64 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))
(+.f64 (.f64 (.f64 (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1) (.f64 (.f64 (.f64 a2 a2) (.f64 (sqrt.f64 1/2) (cos.f64 th))) 1))
(+.f64 (.f64 (.f64 a2 a2) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)) (.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)))
(+.f64 (.f64 (.f64 a1 a1) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)) (.f64 (.f64 a2 a2) (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1)))
(-.f64 (exp.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))) 1)
(/.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.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)))
(/.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))))
(/.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.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))))
(/.f64 (.f64 (cos.f64 th) (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (cos.f64 th) (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 (cos.f64 th) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))) (-.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))))
(/.f64 (.f64 1 (.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)))
(/.f64 (.f64 1 (.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))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (neg.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (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)))))
(/.f64 (.f64 (.f64 (*.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) 1) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (+.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))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (neg.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) 1) (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)))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (hypot.f64 a2 a1)) (sqrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (hypot.f64 a2 a1)) (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (sqrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (cbrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.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)))
(/.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))))
(/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (neg.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (sqrt.f64 1/2) (cos.f64 th))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2)) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))) (cos.f64 th)) (-.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3)) (cos.f64 th)) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))) (cbrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1)
(pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) (hypot.f64 a2 a1)) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 3)
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
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(.f64 (/.f64 (sqrt.f64 1/2) (-.f64 a2 a1)) (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (/.f64 (sqrt.f64 1/2) (-.f64 a2 a1)) (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (/.f64 (sqrt.f64 1/2) (-.f64 a2 a1)) (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))) (cbrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (/.f64 (sqrt.f64 1/2) (-.f64 a2 a1)) (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (/.f64 (sqrt.f64 1/2) (-.f64 a2 a1)) (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) (hypot.f64 a2 a1)) 2)
(pow.f64 (.f64 (hypot.f64 a2 a1) (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 3)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3) 1/3)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 2))
(fabs.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))))
(log.f64 (pow.f64 (exp.f64 (cos.f64 th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))

eval728.0ms (4.6%)

Compiler: Compiled 29829 to 17633 computations (40.9% saved)

prune433.0ms (2.7%)

Pruning

27 alts after pruning (24 fresh and 3 done)

	Pruned	Kept	Total
New	1349	22	1371
Fresh	12	2	14
Picked	1	0	1
Done	2	3	5
Total	1364	27	1391

Error

Counts

1391 → 27

Alt Table

Click to see full alt table

Status	Error	Program
	26.6b	(/.f64 (hypot.f64 a1 a2) (/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 a1 (cos.f64 th))))
	30.2b	(/.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) (cos.f64 th))) (/.f64 1 a2))
✓	26.8b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	44.5b	(/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	30.2b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	42.5b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
▶	26.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	40.5b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	26.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	30.1b	(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
	42.5b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.5b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
▶	42.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	26.8b	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	29.6b	(.f64 (/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	42.5b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
▶	40.5b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	26.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	44.3b	(.f64 (+.f64 1 (.f64 -1/2 (*.f64 th th))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	29.5b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
	30.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
✓	30.2b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	0.7b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	26.7b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
	26.4b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Compiler

Compiled 673 to 501 computations (25.6% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 47 to 17 computations (63.8% saved)

series3.0ms (0%)

Counts

2 → 60

Calls

15 calls:

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

rewrite87.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`associate-*r/`
864×	`distribute-rgt-in`
814×	`distribute-lft-in`
718×	`associate-*l/`
302×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	293	56
2	3802	56

Stop Event

1×	node limit

Counts

2 → 156

Calls

Call 1

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

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1492×	`distribute-lft-in`
1460×	`distribute-rgt-in`
1064×	`associate-/l*`
758×	`associate-r`
736×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	422	11132
1	1123	10306
2	4983	10306

Stop Event

1×	node limit

Counts

216 → 247

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))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1))
(+.f64 (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)) (.f64 1 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1)))
(+.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1) 1) (.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))) 1)
(/.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (hypot.f64 a2 a1) 2)))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (sqrt.f64 1/2)))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (sqrt.f64 1/2) (+.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))))
(/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))) (-.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))
(/.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3)) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))
(/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (.f64 (sqrt.f64 1/2) (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (neg.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (.f64 (sqrt.f64 1/2) (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)))))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 1 (.f64 (sqrt.f64 1/2) (+.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))))
(/.f64 (.f64 1 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2))) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 1 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 1 (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))) (-.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))
(/.f64 (.f64 1 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3))) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 a2 a1)) (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (hypot.f64 a2 a1)) (sqrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 2)) (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
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(/.f64 (.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (cos.f64 th)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (sqrt.f64 1/2)) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)))) (cos.f64 th)) (-.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 3)) (cos.f64 th)) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)))) (sqrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))) (cbrt.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1)
(pow.f64 (.f64 (sqrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) (hypot.f64 a2 a1)) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 3)
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 1/2)) (cos.f64 th)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))

Outputs
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a2 2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (pow.f64 a1 2))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 a2 2)) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -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 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (*.f64 th th)) -1/2))))
(fma.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (*.f64 (sqrt.f64 1/2) -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 -1/720 (.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 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (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 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) -1/2)))))
(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 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 6))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.f64 (sqrt.f64 1/2) -1/2)))))
(.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 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 a1 (.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 1/2)))
(+.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 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)))
(+.f64 (.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)))
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(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3) 1/3)
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 2))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))) 2))
(fabs.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (sqrt.f64 1/2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (cos.f64 th) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))) 1))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series3.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1604×	`add-sqr-sqrt`
1584×	`*-un-lft-identity`
1478×	`add-cube-cbrt`
1458×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	164	28
2	2009	28

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1190×	`associate-*r/`
900×	`unswap-sqr`
880×	`associate-/l*`
712×	`associate-+r-`
670×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	1080
1	296	1068
2	1246	1068
3	7098	1068

Stop Event

1×	node limit

Counts

66 → 69

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))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 a1 (sqrt.f64 2)))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a1 a1) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) a1)
(*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (*.f64 a1 a1) 2))
(log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))) 1)
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(/.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.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 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.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 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.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 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.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 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.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 a1 (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2)))) 1)
(/.f64 a1 (sqrt.f64 2))
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(/.f64 a1 (sqrt.f64 2))
(*.f64 1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) (sqrt.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (pow.f64 2 -1/2)))
(*.f64 a1 (pow.f64 2 -1/2))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a1 a1) 2)))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 a1 (/.f64 2 a1))))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (.f64 a1 (/.f64 a1 2))))
(.f64 (cbrt.f64 (/.f64 (.f64 a1 a1) 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (/.f64 a1 (/.f64 2 a1))))
(.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (cbrt.f64 (.f64 a1 (/.f64 a1 2))))
(*.f64 (pow.f64 2 -1/2) a1)
(*.f64 a1 (pow.f64 2 -1/2))
(*.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a1 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 a1) (cbrt.f64 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a1 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (sqrt.f64 2)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a1) (pow.f64 2 1/4)))
(/.f64 a1 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 (/.f64 a1 (sqrt.f64 2)))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (cbrt.f64 2)))
(pow.f64 (/.f64 a1 (sqrt.f64 2)) 1)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (sqrt.f64 (/.f64 a1 (sqrt.f64 2))) 2)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (cbrt.f64 (/.f64 a1 (sqrt.f64 2))) 3)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3) 1/3)
(/.f64 a1 (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) a1) -1)
(/.f64 a1 (sqrt.f64 2))
(neg.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(sqrt.f64 (/.f64 (*.f64 a1 a1) 2))
(sqrt.f64 (/.f64 a1 (/.f64 2 a1)))
(sqrt.f64 (*.f64 a1 (/.f64 a1 2)))
(log.f64 (exp.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 a1 (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 a1 (sqrt.f64 2)) 3))
(/.f64 a1 (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (/.f64 a1 (sqrt.f64 2))) 1))
(/.f64 a1 (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 a1 (sqrt.f64 2))))
(/.f64 a1 (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))) 1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 a1 (neg.f64 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a1) a1) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) 1) (sqrt.f64 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a1 a1) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a1 (/.f64 (cbrt.f64 2) a1)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a1 (cbrt.f64 (sqrt.f64 2))) (/.f64 a1 (cbrt.f64 2)))
(/.f64 (*.f64 a1 (/.f64 a1 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a1 a1)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 1)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (/.f64 a1 (pow.f64 2 1/4)) 2)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 3)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3) 1/3)
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 2))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 a1) (/.f64 a1 (sqrt.f64 2))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) 3))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2)))) 1))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 25 to 16 computations (36% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite70.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1892×	`add-sqr-sqrt`
1870×	`*-un-lft-identity`
1746×	`add-cube-cbrt`
1728×	`add-cbrt-cube`
190×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	205	17
2	2549	17

Stop Event

1×	node limit

Counts

1 → 40

Calls

Call 1

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

Outputs

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

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1546×	`associate-+r+`
1408×	`distribute-lft-in`
1316×	`associate-+l+`
776×	`associate-*r/`
610×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1198
1	303	1168
2	1095	1126
3	4236	1126

Stop Event

1×	node limit

Counts

52 → 59

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 (exp.f64 (log1p.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) 1)
(*.f64 1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 (.f64 a2 a2) (pow.f64 2 -1/2))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1)
(.f64 (.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2) (*.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2))
(*.f64 (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (cbrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4)))))
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (pow.f64 a2 -2) -1))
(.f64 -1 (/.f64 1 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))))
(.f64 (.f64 (pow.f64 2 -1/2) 1) (*.f64 a2 a2))
(.f64 (.f64 (pow.f64 2 -1/2) a2) a2)
(.f64 (.f64 (pow.f64 2 -1/2) (cbrt.f64 (pow.f64 a2 4))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) a2)) a2)
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 a2 (neg.f64 a2)))
(*.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)))
(*.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)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (/.f64 (pow.f64 2 1/4) a2) -1) (pow.f64 (/.f64 (pow.f64 2 1/4) a2) -1))
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) -1) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) -1))
(pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)) -1)
(pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1)
(pow.f64 (*.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2) 2)
(pow.f64 (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3)
(pow.f64 (pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 3) 1/3)
(sqrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4))))
(log.f64 (exp.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(cbrt.f64 (pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 3))
(expm1.f64 (log1p.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(exp.f64 (log.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(exp.f64 (-.f64 (*.f64 2 (log.f64 a2)) (log.f64 (sqrt.f64 2))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) -1))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1))
(log1p.f64 (expm1.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 1 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 a2 a2) (pow.f64 2 -1/2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(*.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2) (*.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(*.f64 (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (cbrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4)))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (*.f64 1/2 (pow.f64 a2 4))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2)))
(*.f64 (cbrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (*.f64 1/2 (pow.f64 a2 4))))
(.f64 (cbrt.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2)))
(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(*.f64 (pow.f64 2 -1/2) (pow.f64 (pow.f64 a2 -2) -1))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 -1 (/.f64 1 (.f64 (sqrt.f64 2) (neg.f64 (pow.f64 a2 -2)))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (.f64 (pow.f64 2 -1/2) 1) (*.f64 a2 a2))
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) a2) a2)
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(.f64 (.f64 (pow.f64 2 -1/2) (cbrt.f64 (pow.f64 a2 4))) (pow.f64 (cbrt.f64 a2) 2))
(.f64 (pow.f64 2 -1/2) (.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 (cbrt.f64 a2) 2)))
(.f64 (cbrt.f64 (pow.f64 a2 4)) (.f64 (pow.f64 2 -1/2) (pow.f64 (cbrt.f64 a2) 2)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(pow.f64 (/.f64 (pow.f64 2 1/4) a2) -2)
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(/.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(pow.f64 (/.f64 (pow.f64 2 1/4) a2) -2)
(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) a2)) a2)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 a2 (neg.f64 a2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 1) (/.f64 a2 (sqrt.f64 2)))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 1 (cbrt.f64 2)) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(/.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) 1) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)))
(*.f64 (cbrt.f64 (pow.f64 a2 4)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (sqrt.f64 2)))
(/.f64 (*.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 (cbrt.f64 a2) 2)) (sqrt.f64 2))
(*.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)))
(/.f64 (.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 (cbrt.f64 a2) 2)) (.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (cbrt.f64 (pow.f64 a2 4)) (*.f64 (/.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 a2) 2)) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (/.f64 (pow.f64 2 1/4) a2) -1) (pow.f64 (/.f64 (pow.f64 2 1/4) a2) -1))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(pow.f64 (/.f64 (pow.f64 2 1/4) a2) -2)
(.f64 (pow.f64 (cbrt.f64 (/.f64 2 (pow.f64 a2 4))) -1) (pow.f64 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) -1))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (/.f64 1 (cbrt.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2)))))
(/.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 a2 4)))) (cbrt.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2)) -1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 1)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (*.f64 (sqrt.f64 (pow.f64 2 -1/2)) a2) 2)
(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))
(pow.f64 (cbrt.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 3)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 3) 1/3)
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(sqrt.f64 (/.f64 1 (/.f64 2 (pow.f64 a2 4))))
(sqrt.f64 (*.f64 1/2 (pow.f64 a2 4)))
(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))
(log.f64 (exp.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) 3))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (log.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (-.f64 (*.f64 2 (log.f64 a2)) (log.f64 (sqrt.f64 2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) -1))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) 1))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

localize31.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.4b	(.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	3.6b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

Compiler

Compiled 70 to 32 computations (54.3% saved)

series10.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
2.0ms	a2	@	0	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	th	@	0	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	a1	@	0	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
1.0ms	a2	@	inf	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (pow.f64 2 -1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))

rewrite101.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1590×	`associate-*r/`
1322×	`associate-*l/`
418×	`associate-+l+`
370×	`add-sqr-sqrt`
356×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	51
1	366	43
2	4833	43

Stop Event

1×	node limit

Counts

1 → 114

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (+.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (+.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2)) (*.f64 a2 a2)) (*.f64 (*.f64 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(*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) (fma.f64 -1/2 (*.f64 th th) 1)) (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) (fma.f64 -1/2 (*.f64 th th) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2))) (*.f64 (*.f64 a1 a1) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a1 a1) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2))) (*.f64 (*.f64 a2 a2) (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th))) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th))) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (*.f64 -1/2 (*.f64 th th))) (*.f64 (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))) 1)) (*.f64 (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2)))) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) (*.f64 (sqrt.f64 1/2) (*.f64 a1 a1))) (*.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 1/2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (-.f64 1 (*.f64 (pow.f64 th 4) 1/4)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 1) (+.f64 1 (*.f64 1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 th th) 3) -1/8)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 1) (+.f64 1 (+.f64 (*.f64 (pow.f64 th 4) 1/4) (*.f64 1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 th 4) 1/4))) (*.f64 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2))) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))) (sqrt.f64 (+.f64 1 (*.f64 1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 (+.f64 1 (*.f64 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simplify130.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

752×	`associate-l`
722×	`associate-r`
710×	`distribute-lft-neg-in`
696×	`associate-/r/`
680×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	359	10760
1	1050	9936
2	4554	9764

Stop Event

1×	node limit

Counts

150 → 201

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 -1/2 (.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 -1/2 (.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 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1/2 (*.f64 th th))))
(+.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 (.f64 -1/2 (.f64 th th)) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))))
(+.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1/2 (.f64 th th)))))
(+.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 -1/2 (.f64 th th)) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (+.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1/2 (.f64 th th)))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (+.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) (.f64 (.f64 -1/2 (.f64 th th)) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))))
(+.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 (.f64 a2 (sqrt.f64 1/2)))) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))))
(+.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 (.f64 a2 (sqrt.f64 1/2)))))
(+.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1/2 (.f64 th th))) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(+.f64 (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (.f64 a2 a2)) (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (.f64 a1 a1)))
(+.f64 (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (.f64 a1 a1)) (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 (.f64 a2 (sqrt.f64 1/2))) 1) (+.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) 1) (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (.f64 -1/2 (.f64 th th)))))
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(/.f64 (.f64 (.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) (+.f64 1 (.f64 (pow.f64 (.f64 th th) 3) -1/8))) 1) (+.f64 1 (+.f64 (.f64 (pow.f64 th 4) 1/4) (.f64 1/2 (.f64 th th)))))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (.f64 (.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 1/2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a2 a1) 2)))
(/.f64 (.f64 (.f64 (-.f64 1 (.f64 (pow.f64 th 4) 1/4)) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 1) (+.f64 1 (.f64 1/2 (.f64 th th))))
(/.f64 (.f64 (.f64 (+.f64 1 (.f64 (pow.f64 (.f64 th th) 3) -1/8)) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2))) 1) (+.f64 1 (+.f64 (.f64 (pow.f64 th 4) 1/4) (.f64 1/2 (.f64 th th)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 1 (.f64 (pow.f64 th 4) 1/4))) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))) (sqrt.f64 (+.f64 1 (.f64 1/2 (*.f64 th th)))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 th th) 3) -1/8))) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))) (sqrt.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 th 4) 1/4) (.f64 1/2 (*.f64 th th))))))
(/.f64 (.f64 (.f64 (-.f64 1 (.f64 (pow.f64 th 4) 1/4)) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2)) (+.f64 1 (.f64 1/2 (*.f64 th th))))
(/.f64 (.f64 (.f64 (+.f64 1 (.f64 (pow.f64 (.f64 th th) 3) -1/8)) (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2)) (+.f64 1 (+.f64 (.f64 (pow.f64 th 4) 1/4) (.f64 1/2 (*.f64 th th)))))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 1)
(pow.f64 (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (*.f64 (hypot.f64 a2 a1) (pow.f64 2 -1/4))) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))) 3)
(pow.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 2))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2)) (fma.f64 -1/2 (*.f64 th th) 1)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))))))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 3))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 3)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))

Outputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.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 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.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 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.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 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 -1/2 (*.f64 th th)))
(.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (*.f64 (sqrt.f64 1/2) -1/2))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(.f64 -1/2 (.f64 (sqrt.f64 1/2) (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2))))
(.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th)))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (.f64 -1/2 (*.f64 th th)))
(.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (*.f64 (sqrt.f64 1/2) -1/2))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(+.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))) (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))))
(fma.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (.f64 -1/2 (sqrt.f64 1/2)) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 th th))))
(fma.f64 (.f64 (sqrt.f64 1/2) -1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 th th)) (.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 (sqrt.f64 1/2) -1/2) (*.f64 th th))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (.f64 (.f64 a1 a1) (fma.f64 -1/2 (.f64 th th) 1)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 a1 (fma.f64 -1/2 (.f64 th th) 1))))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 th th) 1)) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 a2 (fma.f64 -1/2 (.f64 th th) 1))))
(.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (*.f64 (sqrt.f64 1/2) (pow.f64 a2 2)))
(.f64 (.f64 (.f64 a2 a2) (fma.f64 -1/2 (.f64 th th) 1)) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a2 (.f64 a2 (fma.f64 -1/2 (.f64 th th) 1))))
(.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (fma.f64 a2 a2 (.f64 a1 a1))))
(.f64 (.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1))) (fma.f64 -1/2 (.f64 th th) 1))
(+.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a2 2))) (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (.f64 (sqrt.f64 1/2) (pow.f64 a1 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
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(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 2))
(sqrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1))) 2))
(fabs.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1))))
(log.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2)) (fma.f64 -1/2 (*.f64 th th) 1)))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (pow.f64 (hypot.f64 a2 a1) 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (log.f64 (exp.f64 (sqrt.f64 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2))) 3))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 3) (pow.f64 (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3)))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(cbrt.f64 (.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)) 3) (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 3)))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))) 1))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 (hypot.f64 a2 a1) 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a2 a1) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (fma.f64 -1/2 (*.f64 th th) 1)))

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 th)
	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Compiler

Compiled 27 to 15 computations (44.4% saved)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite83.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1522×	`associate-*l/`
1110×	`*-commutative`
746×	`unswap-sqr`
682×	`swap-sqr`
594×	`associate-/r/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	230	27
2	3112	27

Stop Event

1×	node limit

Counts

1 → 109

Calls

Call 1

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

Outputs

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

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1318×	`associate-/r/`
1196×	`unswap-sqr`
442×	`*-commutative`
432×	`associate-*r/`
412×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	294	4963
1	872	4835
2	3145	4835

Stop Event

1×	node limit

Counts

133 → 165

Calls

Call 1

Inputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (+.f64 (.f64 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 1)
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 1)
(.f64 1 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cos.f64 th)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(.f64 (cbrt.f64 (pow.f64 a1 4)) (.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) 1))
(.f64 (neg.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 2))))
(.f64 (.f64 a1 (neg.f64 a1)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (sqrt.f64 (cos.f64 th)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1)
(.f64 (.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))) (cbrt.f64 (pow.f64 a1 4)))
(.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (*.f64 a1 a1) (cos.f64 th)))
(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 (/.f64 (*.f64 a1 a1) 1) (cos.f64 th)))
(.f64 (/.f64 1 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (.f64 (/.f64 a1 1) (cos.f64 th)) (/.f64 a1 (sqrt.f64 2)))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)) a1)
(.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)) (/.f64 a1 1))
(*.f64 (/.f64 a1 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 a1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (.f64 (/.f64 (*.f64 a1 a1) 1) (cos.f64 th)) (/.f64 1 (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (/.f64 (.f64 a1 a1) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 1 (neg.f64 (sqrt.f64 2))) (.f64 (*.f64 a1 a1) (neg.f64 (cos.f64 th))))
(.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 (/.f64 a1 1) (cos.f64 th)))
(.f64 (/.f64 a1 (sqrt.f64 2)) (.f64 a1 (cos.f64 th)))
(.f64 (/.f64 a1 1) (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 a1 1) (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(*.f64 (/.f64 a1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (/.f64 a1 (cbrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 2)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 1 (cos.f64 th))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 1 (cos.f64 th))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 2)))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1) (.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (cos.f64 th)))
(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2)) (cos.f64 th)) (/.f64 (cbrt.f64 (pow.f64 a1 4)) 1))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))
(.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (.f64 a1 (neg.f64 a1)))
(.f64 (/.f64 (.f64 a1 a1) -1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 a1 (neg.f64 (sqrt.f64 2))) (.f64 a1 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (neg.f64 (cos.f64 th)))) (neg.f64 a1))
(.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (.f64 (sqrt.f64 a1) (cos.f64 th)))) (sqrt.f64 a1))
(.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (.f64 (pow.f64 (cbrt.f64 a1) 2) (cos.f64 th)))) (cbrt.f64 a1))
(.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) 1)) (cos.f64 th))
(.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (pow.f64 a1 4)) (cos.f64 th)))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th)))) (sqrt.f64 a1))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (sqrt.f64 2) (.f64 a1 (cos.f64 th)))) (cbrt.f64 a1))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (sqrt.f64 2) (cos.f64 th))) (pow.f64 (cbrt.f64 a1) 2))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 1) (cos.f64 th))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) 1) (/.f64 (cos.f64 th) 1))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 1 (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) -1) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 (neg.f64 a1)) -1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a1 (neg.f64 a1)) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) 1)) (cos.f64 th))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) -1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))) (*.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))))
(.f64 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a1 (pow.f64 2 1/4))) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a1 (pow.f64 2 1/4))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))) (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))))
(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))) (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1))
(pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 1)
(pow.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 a1 a1) (cos.f64 th))) -1)
(neg.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th))))
(neg.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(neg.f64 (.f64 (.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th))) 1))
(neg.f64 (.f64 1 (.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))
(neg.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (*.f64 a1 (neg.f64 (cos.f64 th))))))
(neg.f64 (/.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))

Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
(*.f64 a1 (/.f64 a1 (sqrt.f64 2)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 2)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))
(fma.f64 -1/2 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 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 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(fma.f64 -1/2 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 th th)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (.f64 a1 (/.f64 a1 (sqrt.f64 2)))))
(fma.f64 -1/2 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 th th)) (fma.f64 1/24 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (pow.f64 th 4)) (.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 -1/720 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 6)) (sqrt.f64 2))) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 a1 2) (pow.f64 th 4)) (sqrt.f64 2))) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a1 a1)) (sqrt.f64 2)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (*.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1)))))
(fma.f64 -1/2 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 th th)) (fma.f64 -1/720 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (pow.f64 th 6)) (fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a1 a1)) (sqrt.f64 2)) (.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(fma.f64 -1/2 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 th th)) (fma.f64 -1/720 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (pow.f64 th 6)) (fma.f64 1/24 (.f64 (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (pow.f64 th 4)) (.f64 a1 (/.f64 a1 (sqrt.f64 2))))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) 1)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 (/.f64 a1 (sqrt.f64 2)) (cos.f64 th)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))) 1)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 1 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (sqrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (cbrt.f64 (/.f64 (.f64 (cos.f64 th) (*.f64 a1 a1)) (sqrt.f64 2))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (/.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(/.f64 (cbrt.f64 (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (pow.f64 a1 4))))
(.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(.f64 (cbrt.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (cbrt.f64 (cos.f64 th)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (cbrt.f64 (pow.f64 a1 4)) (.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (.f64 (cos.f64 th) (pow.f64 (cbrt.f64 a1) 2)) (sqrt.f64 2)))
(.f64 (cos.f64 th) (.f64 (cbrt.f64 (pow.f64 a1 4)) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (cbrt.f64 a1) 2) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a1 4))) (cos.f64 th)))
(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) 1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
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(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a1 (neg.f64 a1)) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) 1) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(*.f64 (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (cos.f64 th) (.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (cbrt.f64 2)) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 (/.f64 a1 (cbrt.f64 2)) a1) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) 1)) (cos.f64 th))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (cos.f64 th)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) (/.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) 1) -1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) 1) (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (/.f64 a1 (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1)))
(.f64 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))) (.f64 a1 (/.f64 a1 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)))) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (.f64 a1 a1) (*.f64 (sqrt.f64 (neg.f64 (sqrt.f64 2))) (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (/.f64 a1 (.f64 (sqrt.f64 (neg.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))) a1))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (.f64 (/.f64 a1 (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (/.f64 a1 (sqrt.f64 (/.f64 (sqrt.f64 2) (cos.f64 th))))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) 1) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(*.f64 (/.f64 a1 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) a1)) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 a1 (/.f64 a1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (.f64 a1 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))))
(/.f64 (.f64 a1 (.f64 a1 (cbrt.f64 (cos.f64 th)))) (*.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (/.f64 a1 (/.f64 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))) a1)) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (.f64 (/.f64 a1 (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (/.f64 a1 (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2))))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (/.f64 (/.f64 (.f64 a1 a1) (cbrt.f64 (neg.f64 (sqrt.f64 2)))) (cbrt.f64 (/.f64 2 (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))) (*.f64 a1 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))))
(*.f64 (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (cos.f64 th) (.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4))))
(.f64 (.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a1 (pow.f64 2 1/4))) (*.f64 (sqrt.f64 (cos.f64 th)) (/.f64 a1 (pow.f64 2 1/4))))
(*.f64 (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (cos.f64 th) (.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))) (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2))))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))) (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))))
(.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))) (.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (cbrt.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (.f64 (sqrt.f64 (cbrt.f64 (.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))) (sqrt.f64 (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))))
(.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2))))) (cbrt.f64 (.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))))) (cbrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2))))
(.f64 (.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1) (*.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4)) a1))
(*.f64 (/.f64 a1 (/.f64 (pow.f64 2 1/4) a1)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 a1 a1) (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.f64 (cos.f64 th) (.f64 (/.f64 a1 (pow.f64 2 1/4)) (/.f64 a1 (pow.f64 2 1/4))))
(pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 1)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (*.f64 a1 (sqrt.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 2)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))) 3)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3) 1/3)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(pow.f64 (/.f64 (sqrt.f64 2) (.f64 (.f64 a1 a1) (cos.f64 th))) -1)
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (.f64 (.f64 a1 a1) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (.f64 (.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th))) 1))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (.f64 1 (.f64 (/.f64 (*.f64 a1 a1) (sqrt.f64 2)) (neg.f64 (cos.f64 th)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) (*.f64 a1 (neg.f64 (cos.f64 th))))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(neg.f64 (/.f64 (*.f64 a1 (neg.f64 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 a1 4) 2) (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (*.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) 3))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))))
(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))

eval472.0ms (3%)

Compiler: Compiled 22515 to 14108 computations (37.3% saved)

prune320.0ms (2%)

Pruning

38 alts after pruning (31 fresh and 7 done)

	Pruned	Kept	Total
New	1038	17	1055
Fresh	5	14	19
Picked	0	1	1
Done	1	6	7
Total	1044	38	1082

Error

Counts

1082 → 38

Alt Table

Click to see full alt table

Status	Error	Program
✓	26.8b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	44.5b	(/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	30.2b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	42.5b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	42.2b	(/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (+.f64 1 (.f64 -1/2 (*.f64 th th)))))
✓	26.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	40.5b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	26.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	30.1b	(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
	42.5b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.5b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	42.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	40.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	42.7b	(/.f64 1 (*.f64 (/.f64 (sqrt.f64 2) a2) (/.f64 1 a2)))
	42.7b	(/.f64 1 (neg.f64 (*.f64 (/.f64 (/.f64 1 a2) (neg.f64 a2)) (sqrt.f64 2))))
	42.5b	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
	29.6b	(.f64 (/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	42.5b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	40.5b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	42.5b	(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) a2)) a2)
▶	26.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	44.3b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	42.2b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
	40.5b	(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
	40.5b	(.f64 (.f64 (neg.f64 a1) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a1)
	26.5b	(.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1)
	55.1b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
▶	55.1b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	26.8b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
	30.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	30.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
✓	30.2b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
✓	0.7b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	26.4b	(.f64 a1 (.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 1/2)))
	26.4b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))
▶	49.2b	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))

Compiler

Compiled 865 to 661 computations (23.6% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 th)
✓	0.2b	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
✓	0.6b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))

Compiler

Compiled 47 to 14 computations (70.2% saved)

series5.0ms (0%)

Counts

2 → 72

Calls

18 calls:

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

rewrite86.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`swap-sqr`
790×	`distribute-rgt-in`
786×	`associate-*r/`
742×	`distribute-lft-in`
584×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	60
1	287	56
2	3612	56

Stop Event

1×	node limit

Counts

2 → 127

Calls

Call 1

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

Outputs

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

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1286×	`distribute-lft-in`
1278×	`associate-/r*`
1026×	`associate-*r/`
914×	`associate-/l/`
856×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	367	9029
1	941	8587
2	3593	8587

Stop Event

1×	node limit

Counts

199 → 215

Calls

Call 1

Inputs
(.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))))
(*.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)))
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(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) 1) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (hypot.f64 a2 a1) (cos.f64 th))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (hypot.f64 a2 a1) (cos.f64 th))) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) 1) (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (/.f64 (*.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) 1) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) 1) (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (.f64 (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) 1) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 1)
(pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (cos.f64 th)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (cos.f64 th) 3)))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))

Outputs
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.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 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.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 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.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 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a1 (*.f64 a1 (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
(.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (fma.f64 a2 a2 (*.f64 a1 a1))))
(*.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 a1 a1 (.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 -1/2 (.f64 th (.f64 th (fma.f64 a1 a1 (.f64 a2 a2)))))))
(fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 -1/2 (.f64 th (.f64 th (fma.f64 a2 a2 (.f64 a1 a1)))))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a1 a1 (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 -1/2 (.f64 th (.f64 th (fma.f64 a1 a1 (*.f64 a2 a2))))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 (sqrt.f64 1/2) (fma.f64 a2 a2 (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (.f64 -1/2 (.f64 th (.f64 th (fma.f64 a2 a2 (*.f64 a1 a1))))))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.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))))))
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(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (cos.f64 th) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (cos.f64 th) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) 1) (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))
(/.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1))))) (sqrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (.f64 (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (.f64 a1 a1)))))) (cbrt.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1)))))
(/.f64 (cos.f64 th) (/.f64 (fma.f64 a2 a2 (neg.f64 (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(.f64 (/.f64 (cos.f64 th) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(.f64 (cos.f64 th) (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))))
(/.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (cos.f64 th)) (+.f64 a2 a1)) (-.f64 a2 a1))
(/.f64 (.f64 (cos.f64 th) (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (-.f64 a2 a1) (+.f64 a1 a2)))
(*.f64 (/.f64 (cos.f64 th) (-.f64 a2 a1)) (/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (+.f64 a1 a2)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) 1) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (cos.f64 th) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (sqrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (cos.f64 th) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (cos.f64 th)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (cos.f64 th) (/.f64 (-.f64 (+.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (pow.f64 (*.f64 a1 a2) 2)) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (cos.f64 th) (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(.f64 (cos.f64 th) (/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 1)
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(pow.f64 (*.f64 (sqrt.f64 (cos.f64 th)) (hypot.f64 a2 a1)) 2)
(pow.f64 (*.f64 (hypot.f64 a2 a1) (sqrt.f64 (cos.f64 th))) 2)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 3)
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(pow.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3) 1/3)
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(sqrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 2))
(sqrt.f64 (pow.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)) 2))
(fabs.f64 (*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)))))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th)) 3))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) (pow.f64 (cos.f64 th) 3)))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(cbrt.f64 (*.f64 (pow.f64 (cos.f64 th) 3) (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3)))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(exp.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))) 1))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (cos.f64 th))))
(*.f64 (cos.f64 th) (pow.f64 (hypot.f64 a2 a1) 2))

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1604×	`add-sqr-sqrt`
1584×	`*-un-lft-identity`
1478×	`add-cube-cbrt`
1458×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	164	28
2	2009	28

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1190×	`associate-*r/`
900×	`unswap-sqr`
880×	`associate-/l*`
712×	`associate-+r-`
670×	`associate-*l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	128	1080
1	296	1068
2	1246	1068
3	7098	1068

Stop Event

1×	node limit

Counts

66 → 69

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2)))) 1)
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(*.f64 1 (/.f64 a2 (sqrt.f64 2)))
(.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a2 a2) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (pow.f64 2 -1/2) a2)
(*.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)
(pow.f64 (/.f64 (sqrt.f64 2) a2) -1)
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (*.f64 a2 a2) 2))
(log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) 1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2)))
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))
(log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2)))) 1)
(/.f64 a2 (sqrt.f64 2))
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(/.f64 a2 (sqrt.f64 2))
(*.f64 1 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(.f64 (sqrt.f64 a2) (.f64 (sqrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) (sqrt.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(.f64 (pow.f64 (cbrt.f64 a2) 2) (.f64 (cbrt.f64 a2) (pow.f64 2 -1/2)))
(*.f64 a2 (pow.f64 2 -1/2))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 (.f64 a2 a2) 2)))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 a2 (/.f64 2 a2))))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (.f64 a2 (/.f64 a2 2))))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (/.f64 a2 (/.f64 2 a2))))
(.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (cbrt.f64 (.f64 a2 (/.f64 a2 2))))
(*.f64 (pow.f64 2 -1/2) a2)
(*.f64 a2 (pow.f64 2 -1/2))
(*.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a2) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a2 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (sqrt.f64 a2) 1) (/.f64 (sqrt.f64 a2) (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (sqrt.f64 a2) (cbrt.f64 2)) (/.f64 (sqrt.f64 a2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (/.f64 1 (cbrt.f64 2)) a2) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 a2 (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) 1) (/.f64 (cbrt.f64 a2) (sqrt.f64 2)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 a2) (pow.f64 2 1/4)))
(/.f64 a2 (sqrt.f64 2))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)) (cbrt.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 (/.f64 a2 (sqrt.f64 2)))) (cbrt.f64 2))
(*.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) (/.f64 (pow.f64 (cbrt.f64 a2) 2) (cbrt.f64 2)))
(pow.f64 (/.f64 a2 (sqrt.f64 2)) 1)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (sqrt.f64 (/.f64 a2 (sqrt.f64 2))) 2)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (cbrt.f64 (/.f64 a2 (sqrt.f64 2))) 3)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3) 1/3)
(/.f64 a2 (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 2) a2) -1)
(/.f64 a2 (sqrt.f64 2))
(neg.f64 (/.f64 a2 (neg.f64 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(sqrt.f64 (/.f64 (*.f64 a2 a2) 2))
(sqrt.f64 (/.f64 a2 (/.f64 2 a2)))
(sqrt.f64 (*.f64 a2 (/.f64 a2 2)))
(log.f64 (exp.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 a2 (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 a2 (sqrt.f64 2)) 3))
(/.f64 a2 (sqrt.f64 2))
(expm1.f64 (log1p.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (/.f64 a2 (sqrt.f64 2))) 1))
(/.f64 a2 (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 a2 (sqrt.f64 2))))
(/.f64 a2 (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))) 1)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 a2 (neg.f64 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (*.f64 (neg.f64 a2) a2) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) 1) (sqrt.f64 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)) (pow.f64 2 1/4))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 a2 a2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 a2 (/.f64 (cbrt.f64 2) a2)) (cbrt.f64 (sqrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 a2 (cbrt.f64 2)))
(/.f64 (*.f64 a2 (/.f64 a2 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (neg.f64 (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2)))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 1)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (/.f64 a2 (pow.f64 2 1/4)) 2)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 3)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3) 1/3)
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(sqrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 2))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 a2) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2))) 3))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (log.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(exp.f64 (.f64 (log.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2)))) 1))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
✓	0.2b	(/.f64 a1 (/.f64 2 a1))
✓	16.8b	(sqrt.f64 (/.f64 a1 (/.f64 2 a1)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite70.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1900×	`add-sqr-sqrt`
1872×	`*-un-lft-identity`
1754×	`add-cube-cbrt`
1732×	`add-cbrt-cube`
182×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	53
1	191	53
2	2447	53

Stop Event

1×	node limit

Counts

3 → 93

Calls

Call 1

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

Outputs

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

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

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

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1414×	`associate-*r/`
1126×	`associate-/l*`
840×	`*-commutative`
690×	`associate-*l/`
658×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2497
1	473	2399
2	1974	2385

Stop Event

1×	node limit

Counts

129 → 126

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 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 (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 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))) 1)
(.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))) 1)
(.f64 1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (pow.f64 (.f64 a1 (*.f64 a1 1/2)) 1/4))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 a1 1/2)))
(*.f64 (sqrt.f64 a1) (/.f64 1 (sqrt.f64 (/.f64 2 a1))))
(.f64 (sqrt.f64 a1) (pow.f64 (.f64 a1 1/2) 1/2))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (cbrt.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2)) (sqrt.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2)))))
(.f64 (sqrt.f64 (.f64 a1 1/2)) (sqrt.f64 a1))
(.f64 (pow.f64 (.f64 a1 1/2) 1/2) (sqrt.f64 a1))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))) 1/2))
(/.f64 1 (sqrt.f64 (/.f64 2 (*.f64 a1 a1))))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 2 a1)) (sqrt.f64 a1)))
(/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1)))
(/.f64 (sqrt.f64 (neg.f64 a1)) (sqrt.f64 (/.f64 -2 a1)))
(/.f64 (neg.f64 (sqrt.f64 a1)) (neg.f64 (sqrt.f64 (/.f64 2 a1))))
(pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/2)
(pow.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) 1)
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) 2)
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) 3)
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3/2) 1/3)
(fabs.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))
(log.f64 (exp.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))))
(cbrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(exp.f64 (log.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (*.f64 a1 1/2))) 1/2))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 1))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 a1 1/2)))) 1)
(.f64 a1 (.f64 a1 1/2))
(.f64 (.f64 a1 (*.f64 a1 1/2)) 1)
(.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 1 (.f64 a1 (*.f64 a1 1/2)))
(.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (*.f64 a1 1/2)))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (pow.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))) 2))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (*.f64 a1 1/2)))
(.f64 (.f64 a1 1/2) a1)
(*.f64 (neg.f64 a1) (/.f64 1 (/.f64 -2 a1)))
(*.f64 1/2 (/.f64 a1 (/.f64 1 a1)))
(.f64 (.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4)) (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4))
(.f64 (.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (cbrt.f64 (.f64 a1 (.f64 a1 1/2)))) (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 (.f64 (*.f64 a1 1/2) 1) a1)
(.f64 (.f64 (*.f64 a1 1/2) (sqrt.f64 a1)) (sqrt.f64 a1))
(.f64 (.f64 (*.f64 a1 1/2) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 a1))
(*.f64 (/.f64 1 (sqrt.f64 (/.f64 2 a1))) (/.f64 a1 (sqrt.f64 (/.f64 2 a1))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (/.f64 a1 (cbrt.f64 (/.f64 2 a1))))
(.f64 (/.f64 a1 1) (.f64 a1 1/2))
(*.f64 (/.f64 a1 -2) (neg.f64 a1))
(*.f64 (/.f64 (sqrt.f64 a1) 2) (/.f64 (sqrt.f64 a1) (/.f64 1 a1)))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (/.f64 2 a1)))
(*.f64 (/.f64 (sqrt.f64 a1) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (/.f64 2 a1))))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 2) (/.f64 (cbrt.f64 a1) (/.f64 1 a1)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (/.f64 2 a1)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 (/.f64 2 a1))) (/.f64 (cbrt.f64 a1) (sqrt.f64 (/.f64 2 a1))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(pow.f64 (.f64 a1 (.f64 a1 1/2)) 1)
(pow.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) 2)
(pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 3)
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 2) 1/2)
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3) 1/3)
(pow.f64 (/.f64 2 (*.f64 a1 a1)) -1)
(neg.f64 (/.f64 a1 (/.f64 -2 a1)))
(sqrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 2))
(log.f64 (pow.f64 (exp.f64 a1) (*.f64 a1 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a1 (.f64 a1 1/2)))))
(cbrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3))
(expm1.f64 (log1p.f64 (.f64 a1 (.f64 a1 1/2))))
(exp.f64 (log.f64 (.f64 a1 (.f64 a1 1/2))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (*.f64 a1 1/2))) 1))
(log1p.f64 (expm1.f64 (.f64 a1 (.f64 a1 1/2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))) 1)
(/.f64 (*.f64 a1 (sqrt.f64 a1)) (sqrt.f64 (/.f64 2 a1)))
(/.f64 (*.f64 (sqrt.f64 a1) a1) (sqrt.f64 (/.f64 2 a1)))
(pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 1)
(pow.f64 (sqrt.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))) 2)
(pow.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))) 3)
(pow.f64 (pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 3) 1/3)
(sqrt.f64 (.f64 (.f64 a1 (.f64 a1 1/2)) (.f64 a1 a1)))
(log.f64 (pow.f64 (exp.f64 a1) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))))
(cbrt.f64 (pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 3))
(expm1.f64 (log1p.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))
(exp.f64 (log.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))) 1))
(log1p.f64 (expm1.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))

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 -1 (.f64 (sqrt.f64 1/2) a1))
(neg.f64 (*.f64 (sqrt.f64 1/2) a1))
(*.f64 (sqrt.f64 1/2) (neg.f64 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 -1 (.f64 (sqrt.f64 1/2) a1))
(neg.f64 (*.f64 (sqrt.f64 1/2) a1))
(*.f64 (sqrt.f64 1/2) (neg.f64 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (pow.f64 a1 2))
(.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 (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) (.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) (.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) (.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) (.f64 a1 (neg.f64 a1)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))) 1)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))) 1)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(.f64 1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (pow.f64 (.f64 a1 (*.f64 a1 1/2)) 1/4))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 a1 1/2)))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 1/2 a1)))
(*.f64 (sqrt.f64 a1) (/.f64 1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1)))
(.f64 (sqrt.f64 a1) (pow.f64 (.f64 a1 1/2) 1/2))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 1/2 a1)))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1)))) (cbrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (cbrt.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))
(.f64 (cbrt.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1)))) (cbrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2)) (sqrt.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2)))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) 2)) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1)))) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(.f64 (sqrt.f64 (.f64 a1 1/2)) (sqrt.f64 a1))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 1/2 a1)))
(.f64 (pow.f64 (.f64 a1 1/2) 1/2) (sqrt.f64 a1))
(.f64 (sqrt.f64 a1) (sqrt.f64 (.f64 1/2 a1)))
(.f64 (pow.f64 1 1/2) (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2) 1/2) (pow.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))) 1/2))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) 2)) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(.f64 (fabs.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1)))) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (sqrt.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1)))))
(/.f64 1 (sqrt.f64 (/.f64 2 (*.f64 a1 a1))))
(/.f64 1 (/.f64 (sqrt.f64 (/.f64 2 a1)) (sqrt.f64 a1)))
(*.f64 (sqrt.f64 a1) (/.f64 1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1)))
(/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1)))
(*.f64 (sqrt.f64 a1) (/.f64 1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (sqrt.f64 (neg.f64 a1)) (sqrt.f64 (/.f64 -2 a1)))
(/.f64 (neg.f64 (sqrt.f64 a1)) (neg.f64 (sqrt.f64 (/.f64 2 a1))))
(*.f64 (sqrt.f64 a1) (/.f64 1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1)))
(pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/2)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(pow.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) 1)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) 2)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(pow.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) 3)
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3/2) 1/3)
(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 a1 a1)) 3/2))
(fabs.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(log.f64 (exp.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(cbrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3/2))
(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 a1 a1)) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(exp.f64 (log.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(exp.f64 (.f64 (log.f64 (.f64 a1 (*.f64 a1 1/2))) 1/2))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 1))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(log1p.f64 (expm1.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(sqrt.f64 (.f64 1/2 (.f64 a1 a1)))
(-.f64 (exp.f64 (log1p.f64 (.f64 a1 (.f64 a1 1/2)))) 1)
(.f64 1/2 (.f64 a1 a1))
(.f64 a1 (.f64 a1 1/2))
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 a1 (*.f64 a1 1/2)) 1)
(.f64 1/2 (.f64 a1 a1))
(.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 1/2 (.f64 a1 a1))
(.f64 1 (.f64 a1 (*.f64 a1 1/2)))
(.f64 1/2 (.f64 a1 a1))
(.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 1/2 (.f64 a1 a1))
(.f64 (sqrt.f64 a1) (.f64 (sqrt.f64 a1) (*.f64 a1 1/2)))
(.f64 1/2 (.f64 a1 a1))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (pow.f64 (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))) 2))
(.f64 1/2 (.f64 a1 a1))
(.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) (.f64 (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1))))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1)))) 4))
(.f64 (pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 2) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 1/2 (.f64 a1 a1))
(.f64 (pow.f64 (cbrt.f64 a1) 2) (.f64 (cbrt.f64 a1) (*.f64 a1 1/2)))
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 a1 1/2) a1)
(.f64 1/2 (.f64 a1 a1))
(*.f64 (neg.f64 a1) (/.f64 1 (/.f64 -2 a1)))
(.f64 1/2 (.f64 a1 a1))
(*.f64 1/2 (/.f64 a1 (/.f64 1 a1)))
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4)) (pow.f64 (.f64 a1 (.f64 a1 1/2)) 1/4))
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) (cbrt.f64 (.f64 a1 (.f64 a1 1/2)))) (cbrt.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 (.f64 1/2 (.f64 a1 a1))))))
(.f64 (cbrt.f64 (.f64 1/2 (.f64 a1 a1))) (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1)))) 4))
(.f64 (.f64 (*.f64 a1 1/2) 1) a1)
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 (*.f64 a1 1/2) (sqrt.f64 a1)) (sqrt.f64 a1))
(.f64 1/2 (.f64 a1 a1))
(.f64 (.f64 (*.f64 a1 1/2) (pow.f64 (cbrt.f64 a1) 2)) (cbrt.f64 a1))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 1 (sqrt.f64 (/.f64 2 a1))) (/.f64 a1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (/.f64 a1 (sqrt.f64 (/.f64 2 a1))) (sqrt.f64 (/.f64 2 a1)))
(/.f64 a1 (*.f64 (sqrt.f64 (/.f64 2 a1)) (sqrt.f64 (/.f64 2 a1))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (/.f64 a1 (cbrt.f64 (/.f64 2 a1))))
(/.f64 (/.f64 a1 (cbrt.f64 (/.f64 2 a1))) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2))
(/.f64 a1 (*.f64 (cbrt.f64 (/.f64 2 a1)) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)))
(.f64 (/.f64 a1 1) (.f64 a1 1/2))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 a1 -2) (neg.f64 a1))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 (sqrt.f64 a1) 2) (/.f64 (sqrt.f64 a1) (/.f64 1 a1)))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 (sqrt.f64 a1) 1) (/.f64 (sqrt.f64 a1) (/.f64 2 a1)))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 (sqrt.f64 a1) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (/.f64 (sqrt.f64 a1) (cbrt.f64 (/.f64 2 a1))))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (/.f64 a1 (cbrt.f64 (/.f64 2 a1))))
(/.f64 (/.f64 a1 (cbrt.f64 (/.f64 2 a1))) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2))
(/.f64 a1 (*.f64 (cbrt.f64 (/.f64 2 a1)) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 2) (/.f64 (cbrt.f64 a1) (/.f64 1 a1)))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) 1) (/.f64 (cbrt.f64 a1) (/.f64 2 a1)))
(.f64 1/2 (.f64 a1 a1))
(*.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (sqrt.f64 (/.f64 2 a1))) (/.f64 (cbrt.f64 a1) (sqrt.f64 (/.f64 2 a1))))
(*.f64 (/.f64 1 (sqrt.f64 (/.f64 2 a1))) (/.f64 a1 (sqrt.f64 (/.f64 2 a1))))
(/.f64 (/.f64 a1 (sqrt.f64 (/.f64 2 a1))) (sqrt.f64 (/.f64 2 a1)))
(/.f64 a1 (*.f64 (sqrt.f64 (/.f64 2 a1)) (sqrt.f64 (/.f64 2 a1))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)) (cbrt.f64 (.f64 a1 (*.f64 a1 1/2))))
(.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1))) (/.f64 (pow.f64 (cbrt.f64 a1) 2) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2)))
(/.f64 (.f64 (cbrt.f64 (.f64 1/2 (*.f64 a1 a1))) (pow.f64 (cbrt.f64 a1) 2)) (pow.f64 (cbrt.f64 (/.f64 2 a1)) 2))
(pow.f64 (.f64 a1 (.f64 a1 1/2)) 1)
(.f64 1/2 (.f64 a1 a1))
(pow.f64 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))) 2)
(.f64 1/2 (.f64 a1 a1))
(pow.f64 (cbrt.f64 (.f64 a1 (.f64 a1 1/2))) 3)
(.f64 1/2 (.f64 a1 a1))
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 2) 1/2)
(.f64 1/2 (.f64 a1 a1))
(pow.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3) 1/3)
(.f64 1/2 (.f64 a1 a1))
(pow.f64 (/.f64 2 (*.f64 a1 a1)) -1)
(.f64 1/2 (.f64 a1 a1))
(neg.f64 (/.f64 a1 (/.f64 -2 a1)))
(.f64 1/2 (.f64 a1 a1))
(sqrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 2))
(.f64 1/2 (.f64 a1 a1))
(log.f64 (pow.f64 (exp.f64 a1) (*.f64 a1 1/2)))
(.f64 1/2 (.f64 a1 a1))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 1/2 (.f64 a1 a1))
(cbrt.f64 (pow.f64 (.f64 a1 (.f64 a1 1/2)) 3))
(.f64 1/2 (.f64 a1 a1))
(expm1.f64 (log1p.f64 (.f64 a1 (.f64 a1 1/2))))
(.f64 1/2 (.f64 a1 a1))
(exp.f64 (log.f64 (.f64 a1 (.f64 a1 1/2))))
(.f64 1/2 (.f64 a1 a1))
(exp.f64 (.f64 (log.f64 (.f64 a1 (*.f64 a1 1/2))) 1))
(.f64 1/2 (.f64 a1 a1))
(log1p.f64 (expm1.f64 (.f64 a1 (.f64 a1 1/2))))
(.f64 1/2 (.f64 a1 a1))
(-.f64 (exp.f64 (log1p.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))) 1)
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(/.f64 (*.f64 a1 (sqrt.f64 a1)) (sqrt.f64 (/.f64 2 a1)))
(/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 (/.f64 2 a1)) a1))
(*.f64 (/.f64 a1 (sqrt.f64 (/.f64 2 a1))) (sqrt.f64 a1))
(*.f64 a1 (/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1))))
(/.f64 (*.f64 (sqrt.f64 a1) a1) (sqrt.f64 (/.f64 2 a1)))
(/.f64 (sqrt.f64 a1) (/.f64 (sqrt.f64 (/.f64 2 a1)) a1))
(*.f64 (/.f64 a1 (sqrt.f64 (/.f64 2 a1))) (sqrt.f64 a1))
(*.f64 a1 (/.f64 (sqrt.f64 a1) (sqrt.f64 (/.f64 2 a1))))
(pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 1)
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(pow.f64 (sqrt.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))) 2)
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(pow.f64 (cbrt.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))) 3)
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(pow.f64 (pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 3) 1/3)
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(sqrt.f64 (.f64 (.f64 a1 (.f64 a1 1/2)) (.f64 a1 a1)))
(sqrt.f64 (.f64 (.f64 a1 a1) (.f64 1/2 (.f64 a1 a1))))
(sqrt.f64 (.f64 a1 (.f64 1/2 (pow.f64 a1 3))))
(sqrt.f64 (*.f64 1/2 (pow.f64 a1 4)))
(log.f64 (pow.f64 (exp.f64 a1) (sqrt.f64 (.f64 a1 (.f64 a1 1/2)))))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))))))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(cbrt.f64 (pow.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2)))) 3))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(expm1.f64 (log1p.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(exp.f64 (log.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(exp.f64 (.f64 (log.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (.f64 a1 1/2))))) 1))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))
(log1p.f64 (expm1.f64 (.f64 a1 (sqrt.f64 (.f64 a1 (*.f64 a1 1/2))))))
(.f64 a1 (sqrt.f64 (.f64 1/2 (*.f64 a1 a1))))

localize14.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 38 to 19 computations (50% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite98.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1542×	`associate-*r/`
1280×	`associate-*l/`
598×	`distribute-lft-in`
556×	`associate-/r*`
412×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	273	28
2	3532	28

Stop Event

1×	node limit

Counts

2 → 208

Calls

Call 1

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

Outputs

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

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

simplify143.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1536×	`associate-/l*`
950×	`times-frac`
760×	`associate-/r*`
686×	`associate-l`
670×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	531	10846
1	1430	10500
2	7946	10500

Stop Event

1×	node limit

Counts

232 → 297

Calls

Call 1

Inputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 1/2))) 1)
(*.f64 1 (sqrt.f64 1/2))
(*.f64 (sqrt.f64 1/2) 1)
(*.f64 (sqrt.f64 (sqrt.f64 1/2)) (sqrt.f64 (sqrt.f64 1/2)))
(*.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2))
(*.f64 (cbrt.f64 1/2) (cbrt.f64 (sqrt.f64 1/2)))
(*.f64 -1 (/.f64 -1 (sqrt.f64 2)))
(*.f64 (/.f64 -1 (sqrt.f64 2)) -1)
(*.f64 (pow.f64 (pow.f64 2 1/4) -1) (pow.f64 (pow.f64 2 1/4) -1))
(*.f64 (pow.f64 (cbrt.f64 2) -1) (pow.f64 (cbrt.f64 (sqrt.f64 2)) -1))
(pow.f64 2 -1/2)
(pow.f64 (sqrt.f64 2) -1)
(pow.f64 (sqrt.f64 1/2) 1)
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(/.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (sqrt.f64 2))
(/.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (pow.f64 2 1/4))
(/.f64 (*.f64 (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 2)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (sqrt.f64 1/2)) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 1/2)) (neg.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 1/2)) (neg.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) 1) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2)))
(/.f64 (.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) 1) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2)))
(/.f64 (*.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))) 1) (-.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))))
(/.f64 (.f64 (+.f64 (pow.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) 3) (pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 3)) 1) (+.f64 (.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))) (-.f64 (.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))))
(/.f64 (.f64 (.f64 -1 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (.f64 (neg.f64 (sqrt.f64 2)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (.f64 (.f64 -1 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (.f64 (neg.f64 (sqrt.f64 2)) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) 1) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) -1) 1) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) 1) 1) (.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)) (sqrt.f64 2)))
(/.f64 (.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) -1) 1) (.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)) (neg.f64 (sqrt.f64 2))))
(/.f64 (*.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (hypot.f64 a1 a2) (sqrt.f64 2))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 (sqrt.f64 -1) (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 (.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 1/2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (*.f64 1 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (*.f64 (hypot.f64 a1 a2) (/.f64 (hypot.f64 a1 a2) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))) 1)
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))) (cbrt.f64 2))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (sqrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (*.f64 (sqrt.f64 1/2) (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) -1) (sqrt.f64 2))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (*.f64 (pow.f64 (hypot.f64 a1 a2) 2) -1) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (sqrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) (.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) 1) (pow.f64 2 1/4))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) -1) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)
(pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 1/2))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))
(cbrt.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (/.f64 1/2 (sqrt.f64 2))))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(fma.f64 (.f64 a1 a1) (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))

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 (pow.f64 a2 2) (sqrt.f64 2)) (/.f64 (pow.f64 a1 2) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 (*.f64 a1 a1) (sqrt.f64 2)))
(/.f64 (pow.f64 a1 2) (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 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
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(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (sqrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
(/.f64 (/.f64 (*.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (sqrt.f64 1/2)) (+.f64 a1 a2)) (-.f64 a1 a2))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 1/2)))
(.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) 1) (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2)))) (sqrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (sqrt.f64 1/2)) (.f64 (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (.f64 a1 a2) 2))))) (cbrt.f64 (-.f64 (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (sqrt.f64 1/2) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) 1) (pow.f64 2 1/4))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/2))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (*.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (sqrt.f64 (cbrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (sqrt.f64 (cbrt.f64 2)) (pow.f64 2 1/4))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (.f64 (sqrt.f64 (cbrt.f64 2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (pow.f64 2 1/4)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/4)) (sqrt.f64 (pow.f64 2 1/4))) (sqrt.f64 (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/2))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) 1) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 (cbrt.f64 2)) (cbrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (.f64 (cbrt.f64 2) (cbrt.f64 (cbrt.f64 2)))))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 (pow.f64 2 1/4)))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 2 1/4))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 2 1/4)) (cbrt.f64 (pow.f64 2 1/4))) (cbrt.f64 2)))
(/.f64 (/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (*.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))) (cbrt.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 1) (neg.f64 (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 2 1/4)) (neg.f64 (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 2)) (neg.f64 (cbrt.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) -1) (sqrt.f64 2))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 (neg.f64 (sqrt.f64 2)))) (sqrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (*.f64 (cbrt.f64 (neg.f64 (sqrt.f64 2))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))) (cbrt.f64 (neg.f64 (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (pow.f64 2 1/4))) (pow.f64 2 1/4))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/2))
(/.f64 (/.f64 (neg.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (neg.f64 (cbrt.f64 2))) (cbrt.f64 (sqrt.f64 2)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (cbrt.f64 2) (cbrt.f64 (sqrt.f64 2))))
(/.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 1)
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(pow.f64 (/.f64 (hypot.f64 a1 a2) (pow.f64 2 1/4)) 2)
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (*.f64 (pow.f64 2 1/4) (pow.f64 2 1/4)))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (pow.f64 2 1/2))
(pow.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 3)
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(pow.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3) 1/3)
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(sqrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2) 1/2))
(sqrt.f64 (*.f64 1/2 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2)))
(sqrt.f64 (*.f64 1/2 (pow.f64 (hypot.f64 a1 a2) 4)))
(log.f64 (pow.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 1/2)))
(*.f64 (/.f64 (sqrt.f64 1/2) 1) (pow.f64 (hypot.f64 a1 a2) 2))
(*.f64 (sqrt.f64 1/2) (pow.f64 (hypot.f64 a1 a2) 2))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) 3))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(cbrt.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) (/.f64 1/2 (sqrt.f64 2))))
(cbrt.f64 (*.f64 (/.f64 1/2 (sqrt.f64 2)) (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3)))
(expm1.f64 (log1p.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(exp.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(exp.f64 (*.f64 (log.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))) 1))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))))
(/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(fma.f64 (.f64 a1 a1) (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(fma.f64 (sqrt.f64 1/2) (.f64 a1 a1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.5b	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	a2	@	0	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))
0.0ms	a2	@	inf	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))
0.0ms	a2	@	-inf	(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1506×	`add-sqr-sqrt`
1486×	`*-un-lft-identity`
1386×	`add-cube-cbrt`
1376×	`add-cbrt-cube`
1358×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	183	17
2	2001	17

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 (pow.f64 a2 4) 1/2))

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

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1126×	`fma-def`
994×	`unswap-sqr`
814×	`distribute-lft-in`
690×	`distribute-rgt-in`
624×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	736
1	148	736
2	409	736
3	1254	736
4	3109	736

Stop Event

1×	node limit

Counts

36 → 28

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 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1)
(.f64 1 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (.f64 a2 (sqrt.f64 (sqrt.f64 1/2))) (*.f64 a2 (sqrt.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (cbrt.f64 (.f64 (pow.f64 a2 4) 1/2)) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (cbrt.f64 (.f64 (pow.f64 a2 4) 1/2)))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4))) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2))))
(.f64 (pow.f64 1 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2)) 1/2))
(pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 1/2)
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)
(pow.f64 (*.f64 a2 (sqrt.f64 (sqrt.f64 1/2))) 2)
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 3/2) 1/3)
(fabs.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))
(log.f64 (exp.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 3/2))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 a2 4) 1/2)) 1/2))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))

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 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 1)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)) 1)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 1 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (.f64 a2 (sqrt.f64 (sqrt.f64 1/2))) (*.f64 a2 (sqrt.f64 (sqrt.f64 1/2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (cbrt.f64 (.f64 (pow.f64 a2 4) 1/2)) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 a2 4))) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) (cbrt.f64 (.f64 (pow.f64 a2 4) 1/2)))
(.f64 (cbrt.f64 (.f64 1/2 (pow.f64 a2 4))) (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4))) (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4))) (sqrt.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 a2 4)))))
(.f64 (pow.f64 1 1/2) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4)) 1/2) (pow.f64 (cbrt.f64 (*.f64 (pow.f64 a2 4) 1/2)) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 a2 8) 1/4))) (sqrt.f64 (cbrt.f64 (*.f64 1/2 (pow.f64 a2 4)))))
(pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 1/2)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)) 1)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (*.f64 a2 (sqrt.f64 (sqrt.f64 1/2))) 2)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))) 3)
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(pow.f64 (pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 3/2) 1/3)
(cbrt.f64 (pow.f64 (*.f64 1/2 (pow.f64 a2 4)) 3/2))
(fabs.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2)))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(log.f64 (exp.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 a2 4) 1/2) 3/2))
(cbrt.f64 (pow.f64 (*.f64 1/2 (pow.f64 a2 4)) 3/2))
(expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(exp.f64 (log.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(exp.f64 (.f64 (log.f64 (.f64 (pow.f64 a2 4) 1/2)) 1/2))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 1/2) (*.f64 a2 a2))) 1))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
(log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/2) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 a2 a2))

eval285.0ms (1.8%)

Compiler: Compiled 14161 to 8731 computations (38.3% saved)

prune200.0ms (1.3%)

Pruning

40 alts after pruning (29 fresh and 11 done)

	Pruned	Kept	Total
New	758	8	766
Fresh	5	21	26
Picked	1	0	1
Done	0	11	11
Total	764	40	804

Error

Counts

804 → 40

Alt Table

Click to see full alt table

Status	Error	Program
✓	26.8b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 2))
	44.5b	(/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	30.2b	(/.f64 (*.f64 a2 a2) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	42.5b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	26.7b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	40.5b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	26.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	30.1b	(/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th))))
	42.5b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	40.5b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
✓	42.6b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	40.5b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	42.7b	(/.f64 1 (*.f64 (/.f64 (sqrt.f64 2) a2) (/.f64 1 a2)))
	42.7b	(/.f64 1 (neg.f64 (*.f64 (/.f64 (/.f64 1 a2) (neg.f64 a2)) (sqrt.f64 2))))
	29.6b	(.f64 (/.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	0.8b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	42.5b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	40.5b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	42.5b	(*.f64 (/.f64 1 (/.f64 (sqrt.f64 2) a2)) a2)
	55.1b	(.f64 (/.f64 1 (sqrt.f64 (/.f64 2 (.f64 a1 a1)))) a1)
✓	26.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	44.3b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	42.2b	(.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (.f64 (sqrt.f64 1/2) (*.f64 a1 a1)))
	55.2b	(.f64 (.f64 (sqrt.f64 1/2) (neg.f64 a1)) a1)
	40.5b	(.f64 (.f64 (sqrt.f64 1/2) a1) a1)
	42.5b	(.f64 (.f64 (neg.f64 a2) (/.f64 1 (neg.f64 (sqrt.f64 2)))) a2)
	42.5b	(.f64 (.f64 a2 a2) (sqrt.f64 1/2))
	26.5b	(.f64 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))) a1)
	55.1b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
✓	55.1b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	26.8b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
✓	0.7b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
	30.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	30.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	55.2b	(.f64 (sqrt.f64 1/2) (.f64 a1 (neg.f64 a1)))
	40.5b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
✓	30.2b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
✓	0.7b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
	26.4b	(.f64 a1 (.f64 (*.f64 a1 (cos.f64 th)) (sqrt.f64 1/2)))
	26.4b	(.f64 a1 (.f64 a1 (*.f64 (sqrt.f64 1/2) (cos.f64 th))))

Compiler

Compiled 491 to 373 computations (24% saved)

regimes269.0ms (1.7%)

Counts

69 → 1

Calls

Call 1

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

Calls

8 calls:

38.0ms	a2
37.0ms	th
36.0ms	a1
32.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
31.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

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	`(cos.f64 th)`
0.4b	1	`(*.f64 a1 a1)`
0.4b	1	`(*.f64 a2 a2)`

Compiler

Compiled 781 to 414 computations (47% saved)

regimes220.0ms (1.4%)

Counts

66 → 1

Calls

Call 1

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

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

Calls

7 calls:

37.0ms	a1
34.0ms	a2
34.0ms	th
28.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
26.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
0.7b	1	`a1`
0.7b	1	`a2`
0.7b	1	`th`
0.7b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.7b	1	`(cos.f64 th)`
0.7b	1	`(*.f64 a1 a1)`
0.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 713 to 379 computations (46.8% saved)

regimes198.0ms (1.2%)

Counts

58 → 1

Calls

Call 1

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

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

Calls

7 calls:

34.0ms	a1
31.0ms	th
28.0ms	a2
26.0ms	(cos.f64 th)
24.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.7b	1	`a1`
0.7b	1	`a2`
0.7b	1	`th`
0.7b	1	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
0.7b	1	`(cos.f64 th)`
0.7b	1	`(*.f64 a1 a1)`
0.7b	1	`(*.f64 a2 a2)`

Compiler

Compiled 592 to 327 computations (44.8% saved)

regimes672.0ms (4.2%)

Counts

55 → 2

Calls

Call 1

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

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

Calls

7 calls:

178.0ms	th
120.0ms	(cos.f64 th)
116.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
75.0ms	a2
68.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.8b	2	`a1`
6.0b	2	`a2`
10.6b	7	`th`
8.8b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
8.8b	6	`(cos.f64 th)`
11.6b	2	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 553 to 315 computations (43% saved)

bsearch42.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
41.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

16.0ms	33×	body	1024	valid
15.0ms	90×	body	256	valid
7.0ms	21×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes609.0ms (3.8%)

Counts

53 → 2

Calls

Call 1

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

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

Calls

7 calls:

156.0ms	th
107.0ms	(cos.f64 th)
104.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
68.0ms	a2
65.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.8b	2	`a1`
6.0b	2	`a2`
10.6b	7	`th`
8.8b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
8.8b	6	`(cos.f64 th)`
11.6b	2	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 533 to 304 computations (43% saved)

bsearch35.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
34.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

17.0ms	104×	body	256	valid
10.0ms	24×	body	1024	valid
5.0ms	16×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes732.0ms (4.6%)

Counts

48 → 2

Calls

Call 1

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

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

Calls

7 calls:

214.0ms	th
128.0ms	a2
100.0ms	a1
95.0ms	(cos.f64 th)
93.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
6.8b	2	`a1`
6.0b	2	`a2`
10.6b	7	`th`
8.8b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
8.8b	6	`(cos.f64 th)`
11.6b	2	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 488 to 285 computations (41.6% saved)

bsearch103.0ms (0.6%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
103.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

38.0ms	87×	body	256	valid
19.0ms	45×	body	1024	valid
3.0ms	12×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes528.0ms (3.3%)

Counts

47 → 2

Calls

Call 1

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

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

Calls

7 calls:

121.0ms	th
102.0ms	(cos.f64 th)
94.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
61.0ms	a2
54.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.8b	2	`a1`
6.0b	2	`a2`
10.6b	6	`th`
8.8b	6	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
8.8b	6	`(cos.f64 th)`
11.6b	2	`(*.f64 a1 a1)`
9.7b	4	`(*.f64 a2 a2)`

Compiler

Compiled 479 to 281 computations (41.3% saved)

bsearch37.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
37.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

16.0ms	96×	body	256	valid
14.0ms	32×	body	1024	valid
5.0ms	16×	body	512	valid

Compiler

Compiled 262 to 200 computations (23.7% saved)

regimes480.0ms (3%)

Counts

40 → 2

Calls

Call 1

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

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

Calls

6 calls:

130.0ms	(cos.f64 th)
104.0ms	th
57.0ms	a2
49.0ms	(*.f64 a2 a2)
35.0ms	a1

Results

Error	Segments	Branch
15.5b	2	`a1`
15.9b	2	`a2`
13.7b	3	`th`
13.6b	2	`(cos.f64 th)`
17.6b	2	`(*.f64 a1 a1)`
18.4b	2	`(*.f64 a2 a2)`

Compiler

Compiled 408 to 243 computations (40.4% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9928866894370053	0.9957047481731763

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes212.0ms (1.3%)

Counts

37 → 2

Calls

Call 1

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

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

Calls

6 calls:

52.0ms	a2
49.0ms	th
37.0ms	a1
27.0ms	(cos.f64 th)
21.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
15.5b	2	`a1`
15.9b	2	`a2`
13.7b	3	`th`
13.6b	2	`(cos.f64 th)`
17.6b	2	`(*.f64 a1 a1)`
18.4b	2	`(*.f64 a2 a2)`

Compiler

Compiled 381 to 229 computations (39.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.9928866894370053	0.9957047481731763

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes89.0ms (0.6%)

Counts

36 → 1

Calls

Call 1

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

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

Calls

5 calls:

19.0ms	a1
18.0ms	a2
18.0ms	th
13.0ms	(*.f64 a2 a2)
11.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
26.8b	1	`a1`
26.8b	1	`a2`
26.8b	1	`th`
26.8b	1	`(*.f64 a1 a1)`
26.8b	1	`(*.f64 a2 a2)`

Compiler

Compiled 367 to 219 computations (40.3% saved)

regimes135.0ms (0.8%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

5 calls:

45.0ms	th
25.0ms	(*.f64 a1 a1)
20.0ms	(*.f64 a2 a2)
20.0ms	a2
20.0ms	a1

Results

Error	Segments	Branch
29.6b	2	`a1`
29.1b	2	`a2`
37.8b	5	`th`
30.8b	4	`(*.f64 a1 a1)`
31.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 149 to 97 computations (34.9% saved)

bsearch39.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
38.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

14.0ms	33×	body	1024	valid
14.0ms	86×	body	256	valid
7.0ms	25×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

regimes72.0ms (0.5%)

Counts

7 → 2

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Error	Segments	Branch
29.6b	2	`a1`
29.1b	2	`a2`
37.8b	5	`th`
30.8b	4	`(*.f64 a1 a1)`
31.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 69 to 48 computations (30.4% saved)

bsearch43.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
43.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

20.0ms	35×	body	1024	valid
14.0ms	88×	body	256	valid
6.0ms	21×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

regimes57.0ms (0.4%)

Accuracy

Total -27.2b remaining (-93.2%)

Threshold costs -27.2b (-93.2%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

5 calls:

19.0ms	th
11.0ms	(*.f64 a1 a1)
10.0ms	(*.f64 a2 a2)
8.0ms	a2
8.0ms	a1

Results

Error	Segments	Branch
29.6b	2	`a1`
29.1b	2	`a2`
37.8b	5	`th`
30.8b	4	`(*.f64 a1 a1)`
31.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 51 to 36 computations (29.4% saved)

bsearch41.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
40.0ms	8.213283828605845e-136	3.7400959148912134e-129

Results

18.0ms	35×	body	1024	valid
15.0ms	92×	body	256	valid
5.0ms	17×	body	512	valid

Compiler

Compiled 208 to 164 computations (21.2% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	682
1	86	682

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(if (<=.f64 a2 3596254329964023/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 2887617409042293/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 413631682916869/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 2887617409042293/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 5434339876390079/3196670515523576044934755563308202297086564498088930458479776726656380660551439995003193449537015778467662777468320381844938727095591204153641140224) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 6867846810695183/12486994201263968925526388919172665222994392570659884603436627838501486955279062480481224412253967884639307724485626491581791902717153141225160704) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 3590010832863391/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))

Outputs
(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(.f64 (cos.f64 th) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)))
(if (<=.f64 a2 3596254329964023/49947976805055875702105555676690660891977570282639538413746511354005947821116249921924897649015871538557230897942505966327167610868612564900642816) (/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) (*.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 2887617409042293/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (.f64 a1 a1))) (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 413631682916869/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 413631682916869/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (sqrt.f64 1/2) (.f64 a1 (cos.f64 th)))) (/.f64 a2 (/.f64 (sqrt.f64 2) (.f64 a2 (cos.f64 th)))))
(if (<=.f64 a2 2887617409042293/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 a2 2887617409042293/780437137578998057845399307448291576437149535666242787714789239906342934704941405030076525765872992789956732780351655723861993919822071326572544) (.f64 a1 (.f64 (sqrt.f64 1/2) (.f64 a1 (cos.f64 th)))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 (.f64 a1 (cos.f64 th)) (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 (sqrt.f64 1/2) (.f64 a1 (cos.f64 th)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (sqrt.f64 1/2) (cos.f64 th)))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (.f64 a2 a2))))
(if (<=.f64 (cos.f64 th) 8962163258467287/9007199254740992) (.f64 a1 (.f64 a1 (.f64 (cos.f64 th) (sqrt.f64 1/2)))) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 1/2))
(if (<=.f64 a2 5434339876390079/3196670515523576044934755563308202297086564498088930458479776726656380660551439995003193449537015778467662777468320381844938727095591204153641140224) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 5434339876390079/3196670515523576044934755563308202297086564498088930458479776726656380660551439995003193449537015778467662777468320381844938727095591204153641140224) (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a2 6867846810695183/12486994201263968925526388919172665222994392570659884603436627838501486955279062480481224412253967884639307724485626491581791902717153141225160704) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2))
(if (<=.f64 a2 6867846810695183/12486994201263968925526388919172665222994392570659884603436627838501486955279062480481224412253967884639307724485626491581791902717153141225160704) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a2 3590010832863391/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(if (<=.f64 a2 3590010832863391/1560874275157996115690798614896583152874299071332485575429578479812685869409882810060153051531745985579913465560703311447723987839644142653145088) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 (.f64 a2 a2) (sqrt.f64 1/2)))
(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
(.f64 (.f64 a1 a1) (sqrt.f64 1/2))

Compiler

Compiled 281 to 194 computations (31% saved)

soundness16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

60×	`fma-def`
50×	`*-commutative`
40×	`associate-/l*`
18×	`associate-/r/`
16×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	39
1	30	35
2	56	35
3	79	35
4	106	35
5	124	35
6	142	35
7	147	35
8	149	35

Stop Event

1×

saturated

Compiler

Compiled 35 to 20 computations (42.9% saved)

end104.0ms (0.7%)

Remove: (sort a1 a2)
Compiler: Compiled 274 to 144 computations (47.4% saved)

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3

Iter	Nodes	Cost
0	27	156
1	72	140
2	146	140
3	208	140
4	286	140
5	334	140
6	382	140
7	395	140
8	401	140
0	3	3
1	3	3