Details

analyze419.0ms (2.7%)

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)

sample4.1s (26.6%)

Results

1.1s	1853×	body	1024	valid
1.0s	5486×	body	256	valid
840.0ms	1603×	body	1024	infinite
422.0ms	909×	body	512	valid
409.0ms	1636×	body	256	infinite
289.0ms	830×	body	512	infinite
5.0ms	8×	body	2048	valid
1.0ms	1×	body	2048	infinite

Bogosity

preprocess19.0ms (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)

simplify15.0ms (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

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

4 alts after pruning (4 fresh and 0 done)

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

Error

0.4b

Counts

5 → 3

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

0.5b

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

▶

0.5b

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

▶

0.5b

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

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize35.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.1b	(.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)

series10.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

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

rewrite85.0ms (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	75
1	280	69
2	3399	69

Stop Event

1×	node limit

Counts

3 → 206

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)))
(fma.f64 a1 a1 (*.f64 a2 a2))

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

simplify139.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac`
950×	`distribute-lft-neg-in`
922×	`associate-r`
822×	`associate-l`
622×	`associate-/l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	517	11182
1	1295	10634
2	6582	10454

Stop Event

1×	node limit

Counts

290 → 312

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

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

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.4b	(.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)

series12.0ms (0.1%)

Counts

3 → 64

Calls

18 calls:

Time	Variable		Point	Expression
8.0ms	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 (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)))

rewrite107.0ms (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	65
1	299	61
2	4071	61

Stop Event

1×	node limit

Counts

3 → 265

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)))
(+.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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(.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 2) (sqrt.f64 2)) (cos.f64 th)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.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 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (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 1 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (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 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)) (cbrt.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2)) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.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 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (-.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)) (/.f64 (cos.f64 th) (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (/.f64 (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (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 (sqrt.f64 2) (cos.f64 th)) (/.f64 1 (+.f64 (pow.f64 a2 4) (-.f64 (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 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (cos.f64 th) (sqrt.f64 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) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (sqrt.f64 2)) (cos.f64 th)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (sqrt.f64 2) (cos.f64 th))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (/.f64 (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (neg.f64 (sqrt.f64 2))) (neg.f64 (cos.f64 th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (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 (neg.f64 (cos.f64 th)) (/.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (hypot.f64 a1 a2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (cos.f64 th)) (/.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 (neg.f64 (cos.f64 th)) (/.f64 (.f64 (neg.f64 (sqrt.f64 2)) (+.f64 (pow.f64 a2 4) (-.f64 (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 (/.f64 (sqrt.f64 2) (cos.f64 th)) (+.f64 (pow.f64 a2 4) (-.f64 (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 4) (pow.f64 a2 4))) (/.f64 (.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (-.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 (cos.f64 th) (pow.f64 (hypot.f64 a1 a2) 2))) (/.f64 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Outputs

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

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1204×	`associate-/r*`
1106×	`associate-r`
1030×	`associate-/l/`
878×	`associate-l`
738×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	719	17331
1	2004	17125

Stop Event

1×	node limit

Counts

329 → 440

Calls

Call 1

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

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 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (.f64 -1/2 (/.f64 (fma.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 (fma.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (/.f64 (.f64 1/24 (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))) (+.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 6))) (+.f64 (fma.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (/.f64 (.f64 1/24 (fma.f64 a2 a2 (.f64 a1 a1))) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))) (+.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 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (sqrt.f64 2)) (cos.f64 th))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
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(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.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 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (pow.f64 (hypot.f64 a1 a2) 2)))
(.f64 (/.f64 (+.f64 (pow.f64 a2 4) (-.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 (hypot.f64 a1 a2) 2))
(.f64 (pow.f64 (hypot.f64 a1 a2) 2) (/.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(.f64 (/.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (sqrt.f64 (+.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 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))))
(.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.f64 (sqrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.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 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(/.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 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(.f64 (/.f64 (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (/.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))) (cbrt.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.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 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)))))
(.f64 (/.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 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(.f64 (cbrt.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (/.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 a1 a1) (.f64 a2 a2))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (.f64 (pow.f64 a1 6) (pow.f64 a1 6)) (.f64 (pow.f64 a2 6) (pow.f64 a2 6))) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (-.f64 (pow.f64 a1 12) (pow.f64 a2 12)) (.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 (pow.f64 a1 12) (pow.f64 a2 12)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6))))
(/.f64 (-.f64 (.f64 (pow.f64 a1 4) (pow.f64 a1 4)) (.f64 (pow.f64 a2 4) (pow.f64 a2 4))) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(/.f64 (-.f64 (pow.f64 a1 8) (pow.f64 a2 8)) (.f64 (-.f64 (.f64 a1 a1) (*.f64 a2 a2)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a1 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (+.f64 (.f64 (pow.f64 a1 6) (pow.f64 a1 6)) (-.f64 (.f64 (pow.f64 a2 6) (pow.f64 a2 6)) (*.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a1 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (+.f64 (pow.f64 a1 12) (-.f64 (pow.f64 a2 12) (*.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a1 6) 3) (pow.f64 (pow.f64 a2 6) 3)) (.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (+.f64 (pow.f64 a1 12) (pow.f64 a2 12)) (*.f64 (pow.f64 a1 6) (pow.f64 a2 6)))))
(/.f64 (-.f64 (pow.f64 (pow.f64 a1 4) 3) (pow.f64 (pow.f64 a2 4) 3)) (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (.f64 (pow.f64 a1 4) (pow.f64 a1 4)) (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (pow.f64 a1 4) (pow.f64 a2 4))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 a1 4) 3) (pow.f64 (pow.f64 a2 4) 3)) (.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)) (+.f64 (pow.f64 a1 8) (+.f64 (pow.f64 a2 8) (.f64 (pow.f64 a1 4) (pow.f64 a2 4))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (neg.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))
(neg.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (neg.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4))) (*.f64 (+.f64 a2 a1) (neg.f64 (-.f64 a1 a2))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6))) (neg.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(-.f64 (/.f64 (pow.f64 a1 4) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (pow.f64 a2 4) (*.f64 (-.f64 a1 a2) (+.f64 a2 a1))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (/.f64 (-.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 (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 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (-.f64 (.f64 a1 a1) (.f64 a2 a2))))))
(/.f64 (/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (+.f64 a1 a2)) (-.f64 a1 a2))
(-.f64 (/.f64 (pow.f64 a1 4) (-.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (pow.f64 a2 4) (*.f64 (-.f64 a1 a2) (+.f64 a2 a1))))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) 1) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (+.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 a1 6) (pow.f64 a2 6)) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))))) (sqrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (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 a1 6) (pow.f64 a2 6)) (.f64 (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 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))) (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2)))))
(/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2)))) (.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)))))))
(/.f64 (/.f64 (+.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (cbrt.f64 (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a2 a1) 2))))) (.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))))))
(pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 1)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a1 a2) 2)) 3)
(pow.f64 (hypot.f64 a1 a2) 2)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3) 1/3)
(pow.f64 (hypot.f64 a1 a2) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 2))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2))))
(pow.f64 (hypot.f64 a1 a2) 2)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a1 a2) 2) 3))
(pow.f64 (hypot.f64 a1 a2) 2)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 a1 a2))))
(pow.f64 (exp.f64 2) (log.f64 (hypot.f64 a1 a2)))
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a1 a2))) 1))
(pow.f64 (exp.f64 2) (log.f64 (hypot.f64 a1 a2)))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a1 a2) 2)))
(pow.f64 (hypot.f64 a1 a2) 2)
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a2 4)) (cbrt.f64 (.f64 a2 a2)) (.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a1 4)) (cbrt.f64 (.f64 a1 a1)) (.f64 a2 a2))

localize23.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 59 to 29 computations (50.8% saved)

series6.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite111.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1568×	`associate-*r/`
1448×	`associate-*l/`
1144×	`associate-/r*`
848×	`associate-/l*`
288×	`add-sqr-sqrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	54
1	286	54
2	3637	54

Stop Event

1×	node limit

Counts

2 → 282

Calls

Call 1

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

Outputs

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

simplify165.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1588×	`times-frac`
934×	`associate-/r/`
796×	`associate-r`
792×	`associate-/r*`
758×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	726	12658
1	1890	12650
2	7806	12650

Stop Event

1×	node limit

Counts

330 → 425

Calls

Call 1

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

eval712.0ms (4.6%)

Compiler: Compiled 30801 to 17614 computations (42.8% saved)

prune459.0ms (3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	1278	17	1295
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	1280	18	1298

Error

Counts

1298 → 18

Alt Table

Click to see full alt table

Status	Error	Program
	26.6b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	0.4b	(/.f64 (hypot.f64 a1 a2) (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) (hypot.f64 a1 a2)))
	34.6b	(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) 1) (-.f64 (.f64 a1 a1) (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (cos.f64 th)))
▶	26.2b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	28.6b	(/.f64 (.f64 (cos.f64 th) (.f64 a1 a1)) (sqrt.f64 2))
	28.6b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	26.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
▶	28.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
▶	26.6b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.4b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	0.8b	(.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)))
	0.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	26.2b	(.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))
	28.6b	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	26.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	0.4b	(.f64 (cos.f64 th) (+.f64 (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (*.f64 (/.f64 a2 (sqrt.f64 2)) a2)))
	0.4b	(.f64 (cos.f64 th) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 2 -1/2)))

Compiler

Compiled 532 to 387 computations (27.3% saved)

localize19.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 46 to 21 computations (54.3% saved)

series6.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	th	@	-inf	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
1.0ms	th	@	0	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	th	@	inf	(*.f64 (pow.f64 2 -1/2) (cos.f64 th))
0.0ms	th	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	a2	@	inf	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite124.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`associate-*r/`
774×	`distribute-rgt-in`
728×	`distribute-lft-in`
630×	`associate-*l/`
328×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	320	48
2	4124	48

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

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

Outputs

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

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

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

846×	`associate-r`
844×	`associate-/l*`
778×	`distribute-lft-neg-in`
778×	`distribute-rgt-neg-in`
768×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	302	7601
1	861	7031
2	5047	6673

Stop Event

1×	node limit

Counts

141 → 152

Calls

Call 1

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

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

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	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	@	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)))

rewrite132.0ms (0.9%)

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

simplify174.0ms (1.1%)

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

localize15.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 12 computations (57.1% saved)

series2.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite65.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1490×	`associate-/r*`
1376×	`associate-/l*`
1064×	`*-commutative`
892×	`associate-*r/`
618×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	224	44
2	2875	44

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

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

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

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1648×	`unswap-sqr`
982×	`associate-/r*`
786×	`associate-/l/`
716×	`associate-/r/`
488×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4350
1	661	4252
2	2487	4214

Stop Event

1×	node limit

Counts

134 → 145

Calls

Call 1

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

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

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	0.2b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	0.4b	(/.f64 a2 (sqrt.f64 2))
✓	0.5b	(/.f64 a1 (sqrt.f64 2))

Compiler

Compiled 60 to 40 computations (33.3% saved)

series3.0ms (0%)

Counts

4 → 24

Calls

12 calls:

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

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1436×	`associate-/r*`
1386×	`associate-*l/`
1132×	`associate-/l*`
1092×	`*-commutative`
686×	`swap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	228	56
2	2913	56

Stop Event

1×	node limit

Counts

4 → 250

Calls

Call 1

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

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1370×	`associate-/l*`
982×	`associate-/l/`
830×	`distribute-rgt-in`
822×	`distribute-lft-in`
582×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	553	5946
1	1346	5514
2	6074	5514

Stop Event

1×	node limit

Counts

274 → 324

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

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

eval577.0ms (3.7%)

Compiler: Compiled 29603 to 18462 computations (37.6% saved)

prune594.0ms (3.8%)

Pruning

24 alts after pruning (21 fresh and 3 done)

	Pruned	Kept	Total
New	1370	19	1389
Fresh	10	2	12
Picked	1	0	1
Done	2	3	5
Total	1383	24	1407

Error

Counts

1407 → 24

Alt Table

Click to see full alt table

Status	Error	Program
▶	43.5b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	26.2b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	44.4b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
▶	40.0b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	28.6b	(/.f64 (.f64 a1 (.f64 (cos.f64 th) a1)) (sqrt.f64 2))
	40.9b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	40.0b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	40.9b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
▶	26.2b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)) a2)
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
✓	28.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	40.9b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	40.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	40.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	26.2b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a2 a2))
	28.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))
▶	0.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	30.9b	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	26.6b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
	26.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	26.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
▶	40.0b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))

Compiler

Compiled 560 to 421 computations (24.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 2)) (cos.f64 th))
✓	0.4b	(.f64 (.f64 (/.f64 1 (sqrt.f64 2)) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	1.0b	(/.f64 1 (sqrt.f64 2))

Compiler

Compiled 51 to 26 computations (49% saved)

series1.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite126.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1852×	`associate-*r/`
1518×	`associate-*l/`
336×	`add-sqr-sqrt`
324×	`pow1`
324×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	50
1	333	48
2	4301	48

Stop Event

1×	node limit

Counts

2 → 163

Calls

Call 1

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

Outputs

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

simplify227.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1874×	`distribute-lft-in`
1108×	`associate-/l*`
912×	`associate-r`
888×	`associate-l`
546×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	466	10183
1	1229	9625
2	6434	9625

Stop Event

1×	node limit

Counts

211 → 262

Calls

Call 1

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

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

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (0.3%)

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	17
1	164	17
2	2009	17

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1534×	`associate-/r/`
790×	`associate-r`
716×	`associate-+r+`
710×	`associate-l`
616×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	592
1	140	592
2	533	592
3	2965	592

Stop Event

1×	node limit

Counts

34 → 26

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

localize7.0ms (0%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite92.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1588×	`add-sqr-sqrt`
1568×	`*-un-lft-identity`
1464×	`add-cube-cbrt`
1448×	`add-cbrt-cube`
158×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	164	17
2	2068	17

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

Outputs

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

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1496×	`associate-r`
1238×	`associate-+r+`
1226×	`associate-l`
1116×	`associate-+l+`
624×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	92	992
1	221	980
2	792	980
3	4996	980

Stop Event

1×	node limit

Counts

46 → 45

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

localize51.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -1/2 (.f64 th th))
✓	0.3b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	10.4b	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2))

Compiler

Compiled 53 to 29 computations (45.3% saved)

series4.0ms (0%)

Counts

3 → 60

Calls

15 calls:

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

rewrite87.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1734×	`associate-*r/`
1696×	`associate-/r*`
1552×	`associate-*l/`
310×	`add-sqr-sqrt`
296×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	313	77
2	3975	77

Stop Event

1×	node limit

Counts

3 → 130

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 a2 a2) (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)) (*.f64 a2 a2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 a2))) (-.f64 1 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 a2 a2))) (-.f64 1 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 -1/2 (*.f64 th th) 1) (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 a2 a2) (*.f64 -1/2 (*.f64 th th))) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (*.f64 (*.f64 -1/2 (*.f64 th th)) (*.f64 a2 a2)) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (/.f64 (fma.f64 -1/2 (*.f64 th th) -1) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 a2) (/.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3)))) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))) (*.f64 a2 a2)) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (*.f64 a2 a2) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1))) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (*.f64 a2 a2) (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) (*.f64 a2 a2))) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 1 (*.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))) (*.f64 a2 a2))) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (*.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1) a2)) (fma.f64 -1/2 (*.f64 th th) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 a2 (*.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))) a2)) (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (-.f64 1 (*.f64 1/4 (pow.f64 th 4)))) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1))) (neg.f64 (fma.f64 -1/2 (*.f64 th th) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 a2 a2) (neg.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (sqrt.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1))) (sqrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) 1)) 2)) (cbrt.f64 (+.f64 1 (*.f64 -1/8 (pow.f64 (*.f64 th th) 3))))) (cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 (*.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) 1)) 2)) (cbrt.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1))) (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 1/4 (pow.f64 th 4))) (*.f64 a2 a2)) (-.f64 1 (*.f64 -1/2 (*.f64 th th))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)) (*.f64 a2 a2)) (neg.f64 (fma.f64 -1/2 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simplify120.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1534×	`unswap-sqr`
812×	`associate-/l*`
520×	`associate-r`
488×	`associate-l`
448×	`distribute-lft-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	342	7980
1	922	7614
2	4632	7614

Stop Event

1×	node limit

Counts

190 → 217

Calls

Call 1

Inputs
(pow.f64 a2 2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 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 (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 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 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 (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 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 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 (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 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(*.f64 -1/2 (pow.f64 th 2))
(+.f64 (.f64 a2 a2) (.f64 (.f64 a2 a2) (.f64 -1/2 (*.f64 th th))))
(+.f64 (.f64 a2 a2) (.f64 (.f64 -1/2 (.f64 th th)) (*.f64 a2 a2)))
(+.f64 (.f64 (.f64 a2 a2) (.f64 -1/2 (.f64 th th))) (*.f64 a2 a2))
(+.f64 (.f64 (.f64 -1/2 (.f64 th th)) (.f64 a2 a2)) (*.f64 a2 a2))
(-.f64 (exp.f64 (log1p.f64 (.f64 a2 a2))) (-.f64 1 (.f64 (.f64 a2 a2) (.f64 -1/2 (*.f64 th th)))))
(-.f64 (exp.f64 (log1p.f64 (.f64 a2 a2))) (-.f64 1 (.f64 (.f64 -1/2 (.f64 th th)) (*.f64 a2 a2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)))) 1)
(-.f64 (+.f64 (.f64 (.f64 a2 a2) (.f64 -1/2 (.f64 th th))) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)
(-.f64 (+.f64 (.f64 (.f64 -1/2 (.f64 th th)) (.f64 a2 a2)) (exp.f64 (log1p.f64 (*.f64 a2 a2)))) 1)
(/.f64 (.f64 a2 a2) (/.f64 (fma.f64 -1/2 (.f64 th th) -1) (+.f64 (*.f64 1/4 (pow.f64 th 4)) -1)))
(/.f64 (.f64 a2 a2) (/.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))))
(/.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2)) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 1 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 1 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 1 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2))) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 1 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2))) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 a2 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) a2)) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 a2 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) a2)) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (.f64 (.f64 a2 a2) (-.f64 1 (.f64 1/4 (pow.f64 th 4)))) (-.f64 1 (.f64 -1/2 (*.f64 th th))))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (neg.f64 (fma.f64 -1/2 (.f64 th th) -1)))
(/.f64 (.f64 (.f64 a2 a2) (neg.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (sqrt.f64 (fma.f64 -1/2 (.f64 th th) -1)))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 th th) 1)) 2)) (cbrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))))) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (pow.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 th th) 1)) 2)) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1))) (cbrt.f64 (fma.f64 -1/2 (.f64 th th) -1)))
(/.f64 (.f64 (-.f64 1 (.f64 1/4 (pow.f64 th 4))) (.f64 a2 a2)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))
(/.f64 (.f64 (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (.f64 a2 a2)) (neg.f64 (fma.f64 -1/2 (.f64 th th) -1)))
(/.f64 (.f64 (neg.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (.f64 a2 a2)) (neg.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) 1) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) 1) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) 1) (fma.f64 -1/2 (*.f64 th th) -1))
(/.f64 (.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2)) 1) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))
(/.f64 (.f64 (sqrt.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (.f64 a2 a2))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th))))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (.f64 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2))) (.f64 a2 a2))) (sqrt.f64 (fma.f64 -1/2 (.f64 th th) -1)))
(/.f64 (.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) a2) a2) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) a2) a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) 1) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (sqrt.f64 (fma.f64 -1/2 (.f64 th th) -1))) (sqrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 th th) -1)) (cbrt.f64 (fma.f64 -1/2 (.f64 th th) -1)))) (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 (.f64 1/4 (pow.f64 th 4)) -1)) (+.f64 1 (.f64 th (sqrt.f64 -1/2)))) (-.f64 (*.f64 th (sqrt.f64 -1/2)) 1))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) 1) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))
(/.f64 (/.f64 (.f64 (.f64 a2 a2) (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))) (.f64 (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))
(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) 1) (fma.f64 -1/2 (.f64 th th) -1))
(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) (sqrt.f64 (fma.f64 -1/2 (.f64 th th) -1))) (sqrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) (.f64 (cbrt.f64 (fma.f64 -1/2 (.f64 th th) -1)) (cbrt.f64 (fma.f64 -1/2 (.f64 th th) -1)))) (cbrt.f64 (fma.f64 -1/2 (*.f64 th th) -1)))
(/.f64 (/.f64 (.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) -1) (.f64 a2 a2)) (+.f64 1 (.f64 th (sqrt.f64 -1/2)))) (-.f64 (*.f64 th (sqrt.f64 -1/2)) 1))
(/.f64 (/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2)) 1) (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (*.f64 th th)))))
(/.f64 (/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2)) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th)))))) (sqrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))
(/.f64 (/.f64 (.f64 (+.f64 1 (.f64 -1/8 (pow.f64 (.f64 th th) 3))) (.f64 a2 a2)) (.f64 (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))) (cbrt.f64 (+.f64 (.f64 1/4 (pow.f64 th 4)) (-.f64 1 (.f64 -1/2 (.f64 th th))))))
(pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)) 1)
(pow.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2))) 3)
(pow.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)) 3) 1/3)
(sqrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4)))
(log.f64 (pow.f64 (exp.f64 (fma.f64 -1/2 (.f64 th th) 1)) (.f64 a2 a2)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)))))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)) 3))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 3) (pow.f64 (*.f64 a2 a2) 3)))
(cbrt.f64 (.f64 (pow.f64 (.f64 a2 a2) 3) (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 3)))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2))))
(exp.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2))) 1))
(log1p.f64 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2))))
(-.f64 (exp.f64 (log1p.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))) 1)
(.f64 1 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2))))
(.f64 (.f64 a2 a2) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)))
(.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2)) (pow.f64 2 -1/2))
(.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2))) 1)
(.f64 (/.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 1/4)) (/.f64 (.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 1/4)))
(.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 -1/2)))
(.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))) (cbrt.f64 (/.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4)) 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4)) 2)) (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4))) (.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2))) (pow.f64 2 -1/2)))
(.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) (/.f64 a2 (sqrt.f64 2)))
(.f64 (pow.f64 2 -1/2) (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2)))
(.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (neg.f64 (.f64 a2 a2))) (/.f64 -1 (sqrt.f64 2)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2)) (pow.f64 2 1/4)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (pow.f64 2 1/4)))
(.f64 (/.f64 (fma.f64 -1/2 (.f64 th th) 1) (sqrt.f64 2)) (*.f64 a2 a2))
(.f64 (/.f64 (fma.f64 -1/2 (.f64 th th) 1) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))
(.f64 (/.f64 (fma.f64 -1/2 (.f64 th th) 1) (pow.f64 2 1/4)) (/.f64 (*.f64 a2 a2) (pow.f64 2 1/4)))
(.f64 (/.f64 (fma.f64 -1/2 (.f64 th th) 1) (cbrt.f64 2)) (/.f64 (*.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 a2) 1) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 a2) (cbrt.f64 2)) (/.f64 (fma.f64 -1/2 (*.f64 th th) 1) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) 1) (/.f64 (.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (cbrt.f64 2)) (/.f64 (.f64 a2 (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2)))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4))) 1) (/.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2))) (sqrt.f64 2)))
(.f64 (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4))) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (.f64 a2 a2))) (pow.f64 2 1/4)))
(.f64 (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4))) (cbrt.f64 2)) (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) 1) (/.f64 a2 (sqrt.f64 2)))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)
(pow.f64 (/.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 1/4)) 2)
(pow.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 3) 1/3)
(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 th th) 1)) -1)
(neg.f64 (/.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4)) 2))
(log.f64 (exp.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 3))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(exp.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))) 1))
(log1p.f64 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(+.f64 (.f64 -1/2 (.f64 th th)) 0)
(+.f64 1 (fma.f64 -1/2 (*.f64 th th) -1))
(-.f64 (fma.f64 -1/2 (*.f64 th th) 1) 1)
(-.f64 (exp.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 th th) 1))) 2)
(-.f64 (/.f64 (.f64 1/4 (pow.f64 th 4)) (fma.f64 -1/2 (.f64 th th) -1)) (+.f64 (/.f64 1 (fma.f64 -1/2 (*.f64 th th) -1)) 1))
(pow.f64 (.f64 -1/2 (.f64 th th)) 1)
(pow.f64 (*.f64 th (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 th th))) 3)
(pow.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)) 1/3)
(sqrt.f64 (*.f64 1/4 (pow.f64 th 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 th th)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 -1/2 (.f64 th th)))))
(cbrt.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 th th))))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 th th))))
(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 th th))) 1))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 th th))))

Outputs
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2)))
(.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th)))
(.f64 a2 (.f64 a2 (.f64 th (.f64 -1/2 th))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2)))
(.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th)))
(.f64 a2 (.f64 a2 (.f64 th (.f64 -1/2 th))))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(+.f64 (pow.f64 a2 2) (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2))
(.f64 (.f64 a2 a2) (fma.f64 -1/2 (*.f64 th th) 1))
(.f64 a2 (.f64 a2 (fma.f64 (*.f64 -1/2 th) th 1)))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2))
(/.f64 (.f64 a2 (.f64 a2 (.f64 th (.f64 -1/2 th)))) (sqrt.f64 2))
(/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 th a2) (*.f64 th a2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2)))
(/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2))
(/.f64 (.f64 a2 (.f64 a2 (.f64 th (.f64 -1/2 th)))) (sqrt.f64 2))
(/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 th a2) (*.f64 th a2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (pow.f64 a2 2) (pow.f64 th 2)) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 (.f64 a2 a2) th) th) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(fma.f64 -1/2 (/.f64 (.f64 (.f64 th a2) (.f64 th a2)) (sqrt.f64 2)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(/.f64 (.f64 (+.f64 1 (.f64 -1/2 (pow.f64 th 2))) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
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(.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))) (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 2) (pow.f64 a2 4))) (cbrt.f64 2)))
(.f64 (cbrt.f64 (.f64 a2 (.f64 (fma.f64 (.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))) (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 (.f64 -1/2 th) th 1) 2) (pow.f64 a2 4))) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))) (/.f64 (cbrt.f64 (.f64 (pow.f64 (fma.f64 (*.f64 -1/2 th) th 1) 2) (pow.f64 a2 4))) (cbrt.f64 2)))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) 1) (/.f64 a2 (sqrt.f64 2)))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) (pow.f64 2 1/4)) (/.f64 a2 (pow.f64 2 1/4)))
(.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (pow.f64 2 1/4) (*.f64 a2 a2))))
(.f64 (/.f64 (.f64 a2 a2) (pow.f64 2 1/4)) (/.f64 (fma.f64 (*.f64 -1/2 th) th 1) (pow.f64 2 1/4)))
(.f64 (/.f64 (.f64 (fma.f64 -1/2 (*.f64 th th) 1) a2) (cbrt.f64 2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (cbrt.f64 (sqrt.f64 2)) (*.f64 a2 a2))))
(.f64 (/.f64 (fma.f64 (.f64 -1/2 th) th 1) (cbrt.f64 2)) (*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) a2))
(pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 1)
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(pow.f64 (/.f64 (.f64 a2 (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) (pow.f64 2 1/4)) 2)
(pow.f64 (/.f64 a2 (/.f64 (pow.f64 2 1/4) (hypot.f64 1 (*.f64 th (sqrt.f64 -1/2))))) 2)
(pow.f64 (.f64 (/.f64 a2 (pow.f64 2 1/4)) (hypot.f64 1 (.f64 th (sqrt.f64 -1/2)))) 2)
(pow.f64 (cbrt.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))) 3)
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(pow.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 3) 1/3)
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (.f64 a2 a2)) (fma.f64 -1/2 (.f64 th th) 1)) -1)
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(neg.f64 (/.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 a2)) (neg.f64 (sqrt.f64 2))))
(/.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (*.f64 a2 (neg.f64 a2))) (neg.f64 (sqrt.f64 2)))
(/.f64 (fma.f64 (.f64 -1/2 th) th 1) (/.f64 (neg.f64 (sqrt.f64 2)) (.f64 a2 (neg.f64 a2))))
(/.f64 (.f64 a2 (neg.f64 a2)) (/.f64 (neg.f64 (sqrt.f64 2)) (fma.f64 (.f64 -1/2 th) th 1)))
(sqrt.f64 (/.f64 (.f64 (pow.f64 (fma.f64 -1/2 (.f64 th th) 1) 2) (pow.f64 a2 4)) 2))
(sqrt.f64 (/.f64 (pow.f64 (fma.f64 -1/2 (*.f64 th th) 1) 2) (/.f64 2 (pow.f64 a2 4))))
(sqrt.f64 (.f64 (/.f64 (pow.f64 (fma.f64 (.f64 -1/2 th) th 1) 2) 2) (pow.f64 a2 4)))
(log.f64 (exp.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(cbrt.f64 (pow.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))) 3))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(expm1.f64 (log1p.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(exp.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))) 1))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(log1p.f64 (expm1.f64 (.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 (*.f64 a2 a2) (sqrt.f64 2)))))
(.f64 (fma.f64 -1/2 (.f64 th th) 1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(.f64 a2 (.f64 (fma.f64 (*.f64 -1/2 th) th 1) (/.f64 a2 (sqrt.f64 2))))
(/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (fma.f64 (.f64 -1/2 th) th 1)))
(+.f64 (.f64 -1/2 (.f64 th th)) 0)
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(+.f64 1 (fma.f64 -1/2 (*.f64 th th) -1))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(-.f64 (fma.f64 -1/2 (*.f64 th th) 1) 1)
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(-.f64 (exp.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 th th) 1))) 2)
(+.f64 (exp.f64 (log1p.f64 (fma.f64 -1/2 (*.f64 th th) 1))) -2)
(+.f64 (exp.f64 (log1p.f64 (fma.f64 (*.f64 -1/2 th) th 1))) -2)
(-.f64 (/.f64 (.f64 1/4 (pow.f64 th 4)) (fma.f64 -1/2 (.f64 th th) -1)) (+.f64 (/.f64 1 (fma.f64 -1/2 (*.f64 th th) -1)) 1))
(-.f64 (/.f64 1/4 (/.f64 (fma.f64 -1/2 (.f64 th th) -1) (pow.f64 th 4))) (+.f64 1 (/.f64 1 (fma.f64 -1/2 (.f64 th th) -1))))
(+.f64 (-.f64 (.f64 (/.f64 1/4 (fma.f64 -1/2 (.f64 th th) -1)) (pow.f64 th 4)) (/.f64 1 (fma.f64 -1/2 (*.f64 th th) -1))) -1)
(+.f64 -1 (+.f64 (.f64 (/.f64 1/4 (fma.f64 -1/2 (.f64 th th) -1)) (pow.f64 th 4)) (/.f64 -1 (fma.f64 -1/2 (*.f64 th th) -1))))
(pow.f64 (.f64 -1/2 (.f64 th th)) 1)
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(pow.f64 (*.f64 th (sqrt.f64 -1/2)) 2)
(pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 th th))) 3)
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(pow.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)) 1/3)
(cbrt.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))
(cbrt.f64 (*.f64 -1/8 (pow.f64 th 6)))
(sqrt.f64 (*.f64 1/4 (pow.f64 th 4)))
(log.f64 (pow.f64 (exp.f64 -1/2) (*.f64 th th)))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(log.f64 (+.f64 1 (expm1.f64 (.f64 -1/2 (.f64 th th)))))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(cbrt.f64 (.f64 -1/8 (pow.f64 (.f64 th th) 3)))
(cbrt.f64 (*.f64 -1/8 (pow.f64 th 6)))
(expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 th th))))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(exp.f64 (log.f64 (.f64 -1/2 (.f64 th th))))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 th th))) 1))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))
(log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 th th))))
(.f64 (.f64 -1/2 th) th)
(.f64 th (.f64 -1/2 th))

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)) a2)
✓	0.4b	(/.f64 (sqrt.f64 2) a2)
✓	0.5b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2))

Compiler

Compiled 30 to 19 computations (36.7% saved)

series4.0ms (0%)

Counts

3 → 48

Calls

15 calls:

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

rewrite85.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1802×	`associate-*l/`
1776×	`associate-/l*`
746×	`associate-/r/`
334×	`distribute-lft-neg-in`
330×	`associate-/l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	59
1	231	59
2	3079	59

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

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

Outputs

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

simplify129.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1178×	`associate-/l*`
1056×	`distribute-lft-in`
846×	`times-frac`
752×	`*-commutative`
748×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	7850
1	1616	7652
2	7281	7652

Stop Event

1×	node limit

Counts

276 → 314

Calls

Call 1

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

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

eval356.0ms (2.3%)

Compiler: Compiled 20260 to 12479 computations (38.4% saved)

prune364.0ms (2.4%)

Pruning

30 alts after pruning (25 fresh and 5 done)

	Pruned	Kept	Total
New	1037	10	1047
Fresh	1	15	16
Picked	0	1	1
Done	3	4	7
Total	1041	30	1071

Error

Counts

1071 → 30

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	28.6b	(/.f64 (.f64 (.f64 (cos.f64 th) a1) a1) (sqrt.f64 2))
✓	26.2b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	44.4b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
	57.9b	(/.f64 (.f64 a2 (.f64 a2 (.f64 (.f64 -1/2 th) th))) (sqrt.f64 2))
✓	40.0b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	40.9b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	40.0b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	40.9b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	40.1b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	57.7b	(/.f64 -1/2 (/.f64 (sqrt.f64 2) (.f64 (.f64 th a2) (*.f64 th a2))))
	40.0b	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
✓	26.2b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)) a2)
✓	28.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
▶	40.9b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	40.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	40.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	26.2b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a2 a2))
	28.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))
	30.9b	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
▶	26.6b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
▶	26.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	26.1b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
✓	40.0b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	40.0b	(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
	40.0b	(.f64 a2 (.f64 (pow.f64 2 -1/2) a2))
	40.0b	(.f64 a2 (.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 a2)))
▶	40.1b	(.f64 a2 (sqrt.f64 (.f64 (/.f64 a2 2) a2)))

Compiler

Compiled 666 to 503 computations (24.5% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 42 to 17 computations (59.5% saved)

series3.0ms (0%)

Counts

3 → 64

Calls

18 calls:

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

rewrite110.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1790×	`associate-/l*`
802×	`associate-/r/`
652×	`associate-/l/`
606×	`distribute-lft-in`
310×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	299	61
2	4065	61

Stop Event

1×	node limit

Counts

3 → 174

Calls

Call 1

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

Outputs

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

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

972×	`times-frac`
936×	`associate-r`
842×	`associate-/l*`
814×	`associate-l`
608×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	498	8746
1	1425	8430

Stop Event

1×	node limit

Counts

238 → 273

Calls

Call 1

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

Outputs
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.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 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.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 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.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 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
(.f64 a1 (.f64 a1 (/.f64 (cos.f64 th) (sqrt.f64 2))))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (/.f64 (.f64 (pow.f64 a1 2) (cos.f64 th)) (sqrt.f64 2)) (/.f64 (.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (sqrt.f64 2))
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
(+.f64 (/.f64 (pow.f64 a2 2) (sqrt.f64 2)) (+.f64 (/.f64 (pow.f64 a1 2) (sqrt.f64 2)) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)) (sqrt.f64 2)))))
(+.f64 (+.f64 (/.f64 (.f64 a2 a2) (sqrt.f64 2)) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 -1/2 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (*.f64 th th)))))
(+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(+.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4))))))
(+.f64 (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 (.f64 1/24 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 th 4))) (sqrt.f64 2))) (+.f64 (/.f64 a2 (/.f64 (sqrt.f64 2) a2)) (/.f64 a1 (/.f64 (sqrt.f64 2) a1))))
(+.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 (fma.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 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (.f64 th th))) (.f64 1/24 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (pow.f64 th 4)))))))
(+.f64 (+.f64 (/.f64 a1 (/.f64 (sqrt.f64 2) a1)) (fma.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (sqrt.f64 2) (fma.f64 a2 a2 (.f64 a1 a1)))) (/.f64 (.f64 1/24 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (pow.f64 th 4))) (sqrt.f64 2)))) (fma.f64 -1/720 (.f64 (/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2)) (pow.f64 th 6)) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(/.f64 (*.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(sqrt.f64 2)
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))))
(+.f64 (sqrt.f64 2) (.f64 1/2 (.f64 (sqrt.f64 2) (*.f64 th th))))
(fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4)))))
(+.f64 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (.f64 (sqrt.f64 2) -5/24)))))
(-.f64 (fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (.f64 -5/24 (pow.f64 th 4))))
(+.f64 (sqrt.f64 2) (+.f64 (.f64 -1 (.f64 (+.f64 (.f64 -1/720 (sqrt.f64 2)) (+.f64 (.f64 1/2 (+.f64 (.f64 1/24 (sqrt.f64 2)) (.f64 -1/4 (sqrt.f64 2)))) (.f64 1/48 (sqrt.f64 2)))) (pow.f64 th 6))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 2) (pow.f64 th 2))) (.f64 -1 (.f64 (+.f64 (.f64 1/24 (sqrt.f64 2)) (*.f64 -1/4 (sqrt.f64 2))) (pow.f64 th 4))))))
(+.f64 (sqrt.f64 2) (fma.f64 -1 (.f64 (pow.f64 th 6) (fma.f64 -1/720 (sqrt.f64 2) (fma.f64 1/2 (.f64 (sqrt.f64 2) -5/24) (.f64 (sqrt.f64 2) 1/48)))) (fma.f64 1/2 (.f64 (sqrt.f64 2) (.f64 th th)) (neg.f64 (.f64 (pow.f64 th 4) (*.f64 (sqrt.f64 2) -5/24))))))
(+.f64 (-.f64 (fma.f64 1/2 (.f64 th (.f64 th (sqrt.f64 2))) (sqrt.f64 2)) (.f64 (sqrt.f64 2) (.f64 -5/24 (pow.f64 th 4)))) (.f64 (pow.f64 th 6) (neg.f64 (fma.f64 (sqrt.f64 2) -1/720 (fma.f64 (sqrt.f64 2) 1/48 (.f64 (sqrt.f64 2) -5/48))))))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a2 2)
(*.f64 a2 a2)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(pow.f64 a1 2)
(*.f64 a1 a1)
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.f64 (pow.f64 a2 2) (pow.f64 a1 2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(+.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)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(+.f64 (.f64 (/.f64 (cos.f64 th) (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)) (fma.f64 a2 a2 (.f64 a1 a1)))
(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2))))) 1)
(*.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (pow.f64 (hypot.f64 a2 a1) 2))
(*.f64 (pow.f64 (hypot.f64 a2 a1) 2) (/.f64 (cos.f64 th) (sqrt.f64 2)))
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(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (/.f64 1 (/.f64 1 (-.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))
(/.f64 (.f64 1 (+.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 (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 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)) (/.f64 1 (/.f64 1 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2))))))
(/.f64 (.f64 1 (+.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 (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 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (/.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(.f64 (/.f64 (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (sqrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(/.f64 (sqrt.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 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (sqrt.f64 (+.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)))) (sqrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (.f64 (hypot.f64 (pow.f64 a1 3) (pow.f64 a2 3)) (hypot.f64 (pow.f64 a1 3) (pow.f64 a2 3))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (.f64 a1 a2) 2))))
(/.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (/.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(/.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (/.f64 (/.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))) (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 (/.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (+.f64 a1 a2)) (/.f64 (cbrt.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (-.f64 a2 a1))))
(/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (cbrt.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))) (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6)))))
(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (cbrt.f64 (+.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)))) (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(.f64 (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (/.f64 (cbrt.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))) (cbrt.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (neg.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4))) (.f64 1 (neg.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (neg.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (*.f64 a2 a1) 2)))))
(/.f64 (.f64 1 (+.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 (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 (neg.f64 (+.f64 (pow.f64 a2 6) (pow.f64 a1 6))) (.f64 1 (neg.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))))))
(/.f64 (.f64 1 (+.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 (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 (-.f64 (.f64 (pow.f64 a2 6) (pow.f64 a2 6)) (.f64 (pow.f64 a1 6) (pow.f64 a1 6))) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a2 a1) 2))) (-.f64 (pow.f64 a2 6) (pow.f64 a1 6))))
(/.f64 (-.f64 (pow.f64 a2 12) (pow.f64 a1 12)) (.f64 (-.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 (pow.f64 a2 12) (pow.f64 a1 12)) (.f64 (-.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 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (-.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (pow.f64 a1 4) (pow.f64 a2 4)) (.f64 1 (-.f64 (.f64 a1 a1) (*.f64 a2 a2))))
(/.f64 (-.f64 (pow.f64 a2 4) (pow.f64 a1 4)) (-.f64 (.f64 a2 a2) (.f64 a1 a1)))
(/.f64 (-.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (.f64 (pow.f64 a1 4) (pow.f64 a1 4))) (.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (pow.f64 a1 4) (pow.f64 a2 4))))
(/.f64 (/.f64 (-.f64 (pow.f64 a2 8) (pow.f64 a1 8)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4)))
(/.f64 (-.f64 (pow.f64 a2 8) (pow.f64 a1 8)) (.f64 (-.f64 (.f64 a2 a2) (*.f64 a1 a1)) (+.f64 (pow.f64 a2 4) (pow.f64 a1 4))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (.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 a2 6)) (-.f64 (.f64 (pow.f64 a1 6) (pow.f64 a1 6)) (*.f64 (pow.f64 a2 6) (pow.f64 a1 6))))))
(/.f64 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (.f64 (+.f64 (pow.f64 a2 4) (-.f64 (pow.f64 a1 4) (pow.f64 (.f64 a1 a2) 2))) (+.f64 (pow.f64 a2 12) (*.f64 (pow.f64 a1 6) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6))))))
(/.f64 (/.f64 (+.f64 (pow.f64 (pow.f64 a2 6) 3) (pow.f64 (pow.f64 a1 6) 3)) (fma.f64 (pow.f64 a1 6) (-.f64 (pow.f64 a1 6) (pow.f64 a2 6)) (pow.f64 a2 12))) (+.f64 (pow.f64 a1 4) (-.f64 (pow.f64 a2 4) (pow.f64 (*.f64 a1 a2) 2))))
(/.f64 (-.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (pow.f64 a1 4) 3)) (.f64 (-.f64 (.f64 a2 a2) (.f64 a1 a1)) (+.f64 (.f64 (pow.f64 a2 4) (pow.f64 a2 4)) (+.f64 (.f64 (pow.f64 a1 4) (pow.f64 a1 4)) (.f64 (pow.f64 a2 4) (pow.f64 a1 4))))))
(/.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (pow.f64 a1 4) 3)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (+.f64 (pow.f64 a2 8) (+.f64 (pow.f64 a1 8) (*.f64 (pow.f64 a2 4) (pow.f64 a1 4)))))
(/.f64 (/.f64 (-.f64 (pow.f64 (pow.f64 a2 4) 3) (pow.f64 (pow.f64 a1 4) 3)) (-.f64 (.f64 a2 a2) (.f64 a1 a1))) (+.f64 (pow.f64 a2 8) (fma.f64 (pow.f64 a2 4) (pow.f64 a1 4) (pow.f64 a1 8))))
(pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 1)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a2 a1) 2)) 3)
(pow.f64 (hypot.f64 a2 a1) 2)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3) 1/3)
(pow.f64 (hypot.f64 a2 a1) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 2))
(sqrt.f64 (pow.f64 (hypot.f64 a2 a1) 4))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2))))
(pow.f64 (hypot.f64 a2 a1) 2)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a2 a1) 2) 3))
(pow.f64 (hypot.f64 a2 a1) 2)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(exp.f64 (*.f64 2 (log.f64 (hypot.f64 a2 a1))))
(pow.f64 (hypot.f64 a2 a1) 2)
(exp.f64 (.f64 (.f64 2 (log.f64 (hypot.f64 a2 a1))) 1))
(pow.f64 (hypot.f64 a2 a1) 2)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a2 a1) 2)))
(pow.f64 (hypot.f64 a2 a1) 2)
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 a1 a1 (*.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a2 a2) (.f64 a1 a1))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 1 (.f64 a1 a1) (.f64 a2 a2))
(fma.f64 a2 a2 (*.f64 a1 a1))
(fma.f64 (cbrt.f64 (pow.f64 a1 4)) (pow.f64 (cbrt.f64 a1) 2) (*.f64 a2 a2))
(fma.f64 (cbrt.f64 (pow.f64 a2 4)) (pow.f64 (cbrt.f64 a2) 2) (*.f64 a1 a1))

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	0.5b	(/.f64 a1 (sqrt.f64 2))

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 a2 (sqrt.f64 (.f64 (/.f64 a2 2) a2)))
✓	20.0b	(sqrt.f64 (*.f64 (/.f64 a2 2) a2))

Compiler

Compiled 27 to 18 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite106.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1718×	`add-sqr-sqrt`
1692×	`*-un-lft-identity`
1580×	`add-cube-cbrt`
1556×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	40
1	186	28
2	2212	28

Stop Event

1×	node limit

Counts

2 → 39

Calls

Call 1

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

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1378×	`associate-+r+`
1310×	`associate-/l*`
1274×	`associate-+l+`
784×	`*-commutative`
742×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1043
1	206	1031
2	864	1023
3	3727	1023

Stop Event

1×	node limit

Counts

63 → 59

Calls

Call 1

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

localize49.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

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 (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)))
0.0ms	a1	@	inf	(.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)))

rewrite64.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1008×	`*-commutative`
908×	`unswap-sqr`
588×	`swap-sqr`
558×	`associate-*r/`
494×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	233	23
2	3025	23

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1666×	`associate-/l*`
1052×	`associate-/r*`
896×	`*-commutative`
620×	`associate-/l/`
570×	`associate-*r/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	3421
1	513	3253
2	2229	3217
3	7955	3217

Stop Event

1×	node limit

Counts

75 → 87

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

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(.f64 (cos.f64 th) (.f64 a2 a2))
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series2.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite95.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1992×	`add-sqr-sqrt`
1974×	`*-un-lft-identity`
1826×	`add-cube-cbrt`
1798×	`add-cbrt-cube`
212×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	218	27
2	2568	27

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1394×	`fma-def`
884×	`associate-+r+`
842×	`associate-+l+`
830×	`distribute-lft-in`
786×	`distribute-rgt-in`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	1181
1	179	1181
2	705	1133
3	1936	1105
4	7072	1105

Stop Event

1×	node limit

Counts

37 → 37

Calls

Call 1

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

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

eval346.0ms (2.2%)

Compiler: Compiled 13942 to 8838 computations (36.6% saved)

prune184.0ms (1.2%)

Pruning

37 alts after pruning (28 fresh and 9 done)

	Pruned	Kept	Total
New	729	14	743
Fresh	6	14	20
Picked	0	1	1
Done	1	8	9
Total	736	37	773

Error

Counts

773 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	40.9b	(/.f64 (/.f64 a1 (/.f64 1 a1)) (sqrt.f64 2))
	40.9b	(/.f64 (/.f64 a1 (sqrt.f64 2)) (/.f64 1 a1))
✓	0.5b	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	28.6b	(/.f64 (.f64 (.f64 (cos.f64 th) a1) a1) (sqrt.f64 2))
✓	26.2b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	44.4b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
✓	40.0b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
	40.9b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	40.0b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	28.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	40.9b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	40.1b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)))
	41.1b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	40.9b	(*.f64 (pow.f64 (/.f64 (sqrt.f64 2) a1) -1) a1)
✓	26.2b	(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)) a2)
✓	28.6b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
✓	40.9b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	40.0b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a2 a2))
	40.9b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	43.5b	(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 (sqrt.f64 1/2) (*.f64 a2 a2)))
	28.5b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))
	40.9b	(.f64 (.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 a1)) a1)
	30.9b	(.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	26.2b	(.f64 (.f64 a2 a2) (*.f64 (sqrt.f64 1/2) (cos.f64 th)))
	53.2b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	53.2b	(.f64 (sqrt.f64 (.f64 (/.f64 a1 2) a1)) a1)
✓	26.6b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	28.5b	(.f64 (sqrt.f64 1/2) (.f64 (*.f64 (cos.f64 th) a1) a1))
✓	26.2b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
	53.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 (neg.f64 a2)))
	40.0b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
	40.9b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
✓	40.0b	(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
	40.0b	(*.f64 a2 (/.f64 1 (/.f64 (sqrt.f64 2) a2)))
	40.0b	(.f64 a2 (.f64 (/.f64 -1 (sqrt.f64 2)) (neg.f64 a2)))
	53.2b	(.f64 a2 (.f64 (sqrt.f64 1/2) (neg.f64 a2)))
	40.0b	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))

Compiler

Compiled 428 to 329 computations (23.1% saved)

regimes224.0ms (1.5%)

Counts

63 → 1

Calls

Call 1

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

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

Calls

8 calls:

31.0ms	a1
31.0ms	a2
30.0ms	th
28.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
26.0ms	(+.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 691 to 384 computations (44.4% saved)

regimes176.0ms (1.1%)

Counts

54 → 1

Calls

Call 1

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

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

Calls

7 calls:

29.0ms	a1
28.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
26.0ms	a2
24.0ms	th
24.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 524 to 299 computations (42.9% saved)

regimes163.0ms (1.1%)

Counts

53 → 1

Calls

Call 1

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

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

Calls

7 calls:

31.0ms	a1
25.0ms	th
24.0ms	a2
21.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
20.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 511 to 295 computations (42.3% saved)

regimes603.0ms (3.9%)

Counts

52 → 2

Calls

Call 1

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

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

Calls

7 calls:

214.0ms	th
89.0ms	a1
87.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
86.0ms	(cos.f64 th)
46.0ms	a2

Results

Error	Segments	Branch
6.8b	2	`a1`
6.1b	2	`a2`
9.8b	6	`th`
11.5b	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
11.5b	4	`(cos.f64 th)`
9.1b	2	`(*.f64 a1 a1)`
8.1b	4	`(*.f64 a2 a2)`

Compiler

Compiled 498 to 291 computations (41.6% saved)

bsearch34.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	1.2378118252379717e-102	2.965302914240246e-98

Results

16.0ms	85×	body	256	valid
8.0ms	26×	body	512	valid
7.0ms	17×	body	1024	valid

Compiler

Compiled 244 to 188 computations (23% saved)

regimes714.0ms (4.6%)

Counts

50 → 2

Calls

Call 1

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

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

Calls

7 calls:

213.0ms	th
122.0ms	(cos.f64 th)
111.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
92.0ms	a1
48.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
6.8b	2	`a1`
6.1b	2	`a2`
9.8b	6	`th`
11.5b	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
11.5b	4	`(cos.f64 th)`
9.1b	2	`(*.f64 a1 a1)`
8.1b	4	`(*.f64 a2 a2)`

Compiler

Compiled 478 to 281 computations (41.2% saved)

bsearch33.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	1.2378118252379717e-102	2.965302914240246e-98

Results

13.0ms	27×	body	1024	valid
13.0ms	85×	body	256	valid
5.0ms	16×	body	512	valid

Compiler

Compiled 236 to 180 computations (23.7% saved)

regimes339.0ms (2.2%)

Counts

38 → 2

Calls

Call 1

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

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

Calls

6 calls:

108.0ms	th
74.0ms	(cos.f64 th)
56.0ms	(*.f64 a2 a2)
36.0ms	a2
35.0ms	a1

Results

Error	Segments	Branch
6.9b	2	`a1`
6.1b	2	`a2`
9.8b	6	`th`
11.5b	4	`(cos.f64 th)`
9.1b	2	`(*.f64 a1 a1)`
8.2b	4	`(*.f64 a2 a2)`

Compiler

Compiled 362 to 224 computations (38.1% saved)

bsearch33.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
32.0ms	1.2378118252379717e-102	2.965302914240246e-98

Results

14.0ms	84×	body	256	valid
9.0ms	22×	body	1024	valid
6.0ms	22×	body	512	valid

Compiler

Compiled 236 to 180 computations (23.7% saved)

regimes296.0ms (1.9%)

Counts

36 → 2

Calls

Call 1

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

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

Calls

6 calls:

100.0ms	th
62.0ms	(cos.f64 th)
38.0ms	a2
33.0ms	(*.f64 a2 a2)
32.0ms	a1

Results

Error	Segments	Branch
6.9b	2	`a1`
6.1b	2	`a2`
9.8b	6	`th`
11.5b	4	`(cos.f64 th)`
9.1b	2	`(*.f64 a1 a1)`
8.2b	4	`(*.f64 a2 a2)`

Compiler

Compiled 344 to 216 computations (37.2% saved)

bsearch37.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
36.0ms	1.2378118252379717e-102	2.965302914240246e-98

Results

17.0ms	40×	body	1024	valid
12.0ms	69×	body	256	valid
6.0ms	19×	body	512	valid

Compiler

Compiled 236 to 180 computations (23.7% saved)

regimes187.0ms (1.2%)

Counts

35 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

6 calls:

48.0ms	th
31.0ms	a1
30.0ms	a2
26.0ms	(*.f64 a1 a1)
24.0ms	(cos.f64 th)

Results

Error	Segments	Branch
16.3b	2	`a1`
15.2b	2	`a2`
13.5b	3	`th`
13.5b	2	`(cos.f64 th)`
17.8b	2	`(*.f64 a1 a1)`
16.9b	2	`(*.f64 a2 a2)`

Compiler

Compiled 335 to 212 computations (36.7% saved)

bsearch54.0ms (0.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
24.0ms	0.0002944450571395368	5412.98581011242
29.0ms	-8.432025361506778e-25	-2.8858551921075502e-33

Results

49.0ms

288×

body

256

valid

Compiler

Compiled 658 to 488 computations (25.8% saved)

regimes76.0ms (0.5%)

Counts

34 → 1

Calls

Call 1

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

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

Calls

5 calls:

17.0ms	a2
16.0ms	th
16.0ms	a1
10.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
26.6b	1	`a1`
26.6b	1	`a2`
26.6b	1	`th`
26.6b	1	`(*.f64 a1 a1)`
26.6b	1	`(*.f64 a2 a2)`

Compiler

Compiled 321 to 202 computations (37.1% saved)

regimes150.0ms (1%)

Counts

25 → 2

Calls

Call 1

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

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

Calls

5 calls:

56.0ms	th
33.0ms	a1
24.0ms	a2
18.0ms	(*.f64 a1 a1)
13.0ms	(*.f64 a2 a2)

Results

Error	Segments	Branch
29.8b	2	`a1`
29.2b	2	`a2`
36.6b	4	`th`
31.2b	2	`(*.f64 a1 a1)`
31.4b	2	`(*.f64 a2 a2)`

Compiler

Compiled 207 to 138 computations (33.3% saved)

bsearch23.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
22.0ms	1.1650369278793073e-145	3.569629650171053e-145

Results

10.0ms	20×	body	1024	valid
7.0ms	45×	body	256	valid
4.0ms	15×	body	512	valid

Compiler

Compiled 138 to 105 computations (23.9% saved)

regimes172.0ms (1.1%)

Counts

13 → 2

Calls

Call 1

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

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

Calls

5 calls:

52.0ms	a2
44.0ms	(*.f64 a2 a2)
35.0ms	th
24.0ms	a1
12.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
29.8b	2	`a1`
29.2b	2	`a2`
36.6b	4	`th`
31.2b	2	`(*.f64 a1 a1)`
31.4b	2	`(*.f64 a2 a2)`

Compiler

Compiled 109 to 72 computations (33.9% saved)

bsearch21.0ms (0.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
21.0ms	1.1650369278793073e-145	3.569629650171053e-145

Results

9.0ms	51×	body	256	valid
7.0ms	17×	body	1024	valid
4.0ms	12×	body	512	valid

Compiler

Compiled 128 to 100 computations (21.9% saved)

regimes12.0ms (0.1%)

Accuracy

Total -0.1b remaining (-0.2%)

Threshold costs -0.1b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	a1
3.0ms	th
3.0ms	a2

Results

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

Compiler

Compiled 27 to 20 computations (25.9% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

40×	`*-commutative`
4×	`+-commutative`
2×	`1-exp`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	633
1	105	633

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a2 278969282152207/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (.f64 a1 a1)) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 278969282152207/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) a1) a1)) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 2019352817565217/2462625387274654950767440006258975862817483704404090416746768337765357610718575663213391640930307227550414249394176) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 8826049387992363/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 th -8929009308005425/10889035741470030830827987437816582766592) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 th 5908722711110091/72057594037927936) (.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a2 2390047953351073/7029552803973744348141466418259346654483901747346744739219930582205996219799199797373501072037329464296751422864876398630012915711709843264075804970101818523648) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (sqrt.f64 (.f64 (/.f64 a2 2) a2))))
(if (<=.f64 a2 4920686962781621/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))

Outputs
(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2)))
(if (<=.f64 a2 278969282152207/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (.f64 a1 a1)) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 278969282152207/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 (sqrt.f64 1/2) (.f64 (.f64 (cos.f64 th) a1) a1)) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 278969282152207/19239260838083241802870625048898248928261591440656956380834127638791856333738872368854622194768025215237611323392) (.f64 (sqrt.f64 1/2) (.f64 a1 (.f64 (cos.f64 th) a1))) (.f64 (cos.f64 th) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 2019352817565217/2462625387274654950767440006258975862817483704404090416746768337765357610718575663213391640930307227550414249394176) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))
(if (<=.f64 a2 8826049387992363/2521728396569246669585858566409191283525103313309788586748690777871726193375821479130513040312634601011624191379636224) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))
(if (<=.f64 th -8929009308005425/10889035741470030830827987437816582766592) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 th 5908722711110091/72057594037927936) (.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(if (or (<=.f64 th -8929009308005425/10889035741470030830827987437816582766592) (not (<=.f64 th 5908722711110091/72057594037927936))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 -1/2 (*.f64 th th)) 1))))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 1/2))
(if (<=.f64 a2 2390047953351073/7029552803973744348141466418259346654483901747346744739219930582205996219799199797373501072037329464296751422864876398630012915711709843264075804970101818523648) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (sqrt.f64 (.f64 (/.f64 a2 2) a2))))
(if (<=.f64 a2 2390047953351073/7029552803973744348141466418259346654483901747346744739219930582205996219799199797373501072037329464296751422864876398630012915711709843264075804970101818523648) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 a2 (sqrt.f64 (.f64 a2 (/.f64 a2 2)))))
(if (<=.f64 a2 4920686962781621/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(if (<=.f64 a2 4920686962781621/14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203637047296) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (*.f64 a2 (/.f64 a2 (sqrt.f64 2))))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Compiler

Compiled 260 to 183 computations (29.6% saved)

soundness59.0ms (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

Compiler

Compiled 35 to 20 computations (42.9% saved)

end134.0ms (0.9%)

Remove: (sort a1 a2)
Compiler: Compiled 258 to 144 computations (44.2% 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