Details

analyze399.0ms (2.8%)

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)

sample3.9s (27.3%)

Results

1.0s	5469×	body	256	valid
948.0ms	1870×	body	1024	valid
897.0ms	1651×	body	1024	infinite
402.0ms	788×	body	512	infinite
323.0ms	1615×	body	256	infinite
319.0ms	912×	body	512	valid
3.0ms	5×	body	2048	valid

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)))

eval29.0ms (0.2%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

5 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
▶	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Status

Error

Program

▶

0.5b

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

▶

0.5b

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

▶

0.4b

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

Compiler

Compiled 46 to 31 computations (32.6% saved)

localize15.0ms (0.1%)

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
2.0ms	a2	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	th	@	inf	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
1.0ms	a1	@	0	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
1.0ms	th	@	0	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

rewrite125.0ms (0.9%)

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)))))))

simplify134.0ms (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)

localize47.0ms (0.3%)

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)

series4.0ms (0%)

Counts

3 → 64

Calls

18 calls:

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

rewrite137.0ms (1%)

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 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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))))))

simplify186.0ms (1.3%)

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))

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 37 to 16 computations (56.8% saved)

series1.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite77.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1130×	`associate-*r/`
900×	`associate-*l/`
818×	`associate-/r*`
614×	`associate-/l*`
482×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	280	33
2	3405	33

Stop Event

1×	node limit

Counts

1 → 150

Calls

Call 1

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

Outputs

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

simplify133.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1408×	`associate-/l*`
722×	`times-frac`
604×	`distribute-lft-in`
596×	`distribute-lft-neg-in`
596×	`distribute-rgt-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	439	9180
1	1135	8828
2	5961	8436

Stop Event

1×	node limit

Counts

186 → 230

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

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

eval501.0ms (3.5%)

Compiler: Compiled 23578 to 13841 computations (41.3% saved)

prune330.0ms (2.3%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1088	17	1105
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	1089	19	1108

Error

Counts

1108 → 19

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	24.2b	(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (sqrt.f64 2))
	36.0b	(/.f64 (-.f64 (.f64 (.f64 a1 a1) (.f64 a1 a1)) (pow.f64 a2 4)) (/.f64 (.f64 (+.f64 a1 a2) (-.f64 a1 a2)) (/.f64 (cos.f64 th) (sqrt.f64 2))))
▶	24.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
▶	26.9b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	29.5b	(/.f64 (.f64 a1 (.f64 a1 (cos.f64 th))) (sqrt.f64 2))
	0.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (pow.f64 (hypot.f64 a1 a2) 2)))
	29.5b	(/.f64 a1 (/.f64 (sqrt.f64 2) (*.f64 a1 (cos.f64 th))))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	26.9b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
▶	29.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
	24.3b	(.f64 (/.f64 1 (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	0.7b	(.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)))) 1) (+.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)))
▶	0.9b	(.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)))
	29.5b	(.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2)))
	26.9b	(*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
	0.5b	(.f64 (cos.f64 th) (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (pow.f64 2 -1/2)))

Compiler

Compiled 545 to 391 computations (28.3% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 37 to 16 computations (56.8% saved)

series5.0ms (0%)

Counts

3 → 64

Calls

18 calls:

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

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1574×	`associate-*r/`
1460×	`associate-/l*`
1242×	`associate-*l/`
492×	`associate-/r/`
292×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	65
1	286	61
2	3645	61

Stop Event

1×	node limit

Counts

3 → 145

Calls

Call 1

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

Outputs

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

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

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

simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1732×	`distribute-lft-in`
702×	`times-frac`
692×	`associate-/l*`
662×	`associate-r`
596×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	394	7373
1	1083	7041
2	5570	7037

Stop Event

1×	node limit

Counts

209 → 227

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

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 31 to 12 computations (61.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite63.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 51

Calls

Call 1

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

Outputs

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

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

75 → 78

Calls

Call 1

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

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

localize13.0ms (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)

series3.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite70.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1030×	`*-commutative`
922×	`associate-*r/`
848×	`associate-/r*`
782×	`unswap-sqr`
754×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	224	27
2	2793	27

Stop Event

1×	node limit

Counts

1 → 113

Calls

Call 1

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

Outputs

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

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1224×	`associate-/l*`
752×	`associate-/l/`
730×	`unswap-sqr`
540×	`times-frac`
450×	`distribute-frac-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	5039
1	934	5039
2	4971	4895

Stop Event

1×	node limit

Counts

137 → 171

Calls

Call 1

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

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

localize11.0ms (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)

series4.0ms (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))
1.0ms	th	@	-inf	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
1.0ms	a2	@	0	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
0.0ms	th	@	0	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
0.0ms	a2	@	inf	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))

rewrite69.0ms (0.5%)

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))))))))

simplify72.0ms (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)))))
(fma.f64 1/24 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (pow.f64 th 4)) (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 (fma.f64 -1/2 (/.f64 (.f64 (.f64 th th) (.f64 a2 a2)) (sqrt.f64 2)) (/.f64 (.f64 -1/720 (.f64 (pow.f64 th 6) (.f64 a2 a2))) (sqrt.f64 2))) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
(fma.f64 1/24 (/.f64 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (sqrt.f64 2)) (+.f64 (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (.f64 -1/720 (/.f64 (.f64 (pow.f64 th 6) (.f64 a2 a2)) (sqrt.f64 2)))) (*.f64 a2 (/.f64 a2 (sqrt.f64 2)))))
(+.f64 (fma.f64 1/24 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (pow.f64 th 4)) (fma.f64 -1/2 (.f64 (.f64 a2 (/.f64 a2 (sqrt.f64 2))) (.f64 th th)) (.f64 a2 (/.f64 a2 (sqrt.f64 2))))) (.f64 -1/720 (/.f64 (.f64 a2 a2) (/.f64 (sqrt.f64 2) (pow.f64 th 6)))))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 a2 2)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(/.f64 (*.f64 (pow.f64 a2 2) (cos.f64 th)) (sqrt.f64 2))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(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 -1/2 (.f64 (.f64 th th) (.f64 a2 a2))) (*.f64 a2 a2))
(.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2))
(.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2)))
(+.f64 (pow.f64 a2 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 th 2) (pow.f64 a2 2))) (.f64 1/24 (.f64 (pow.f64 th 4) (pow.f64 a2 2)))))
(+.f64 (fma.f64 -1/2 (.f64 (.f64 th th) (.f64 a2 a2)) (.f64 1/24 (.f64 (pow.f64 th 4) (.f64 a2 a2)))) (*.f64 a2 a2))
(fma.f64 a2 a2 (.f64 (.f64 a2 a2) (+.f64 (.f64 -1/2 (.f64 th th)) (*.f64 1/24 (pow.f64 th 4)))))
(.f64 (.f64 a2 a2) (+.f64 (+.f64 1 (.f64 -1/2 (.f64 th th))) (*.f64 1/24 (pow.f64 th 4))))
(+.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 (fma.f64 -1/2 (.f64 (.f64 th th) (.f64 a2 a2)) (fma.f64 1/24 (.f64 (pow.f64 th 4) (.f64 a2 a2)) (.f64 -1/720 (.f64 (pow.f64 th 6) (.f64 a2 a2))))) (*.f64 a2 a2))
(fma.f64 a2 a2 (fma.f64 -1/2 (.f64 (.f64 th th) (.f64 a2 a2)) (.f64 (.f64 a2 a2) (+.f64 (.f64 1/24 (pow.f64 th 4)) (*.f64 -1/720 (pow.f64 th 6))))))
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(.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))
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(.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 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))) (/.f64 (pow.f64 2 1/4) (/.f64 (cbrt.f64 (.f64 a2 (*.f64 a2 (cos.f64 th)))) (pow.f64 2 1/4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (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))) (pow.f64 2 1/4)) (/.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))) (/.f64 (pow.f64 2 1/4) (/.f64 (cbrt.f64 (.f64 a2 (*.f64 a2 (cos.f64 th)))) (pow.f64 2 1/4))))
(.f64 (/.f64 (cbrt.f64 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)) (pow.f64 2 1/4)) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (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 (cbrt.f64 (.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))) (/.f64 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))) (cbrt.f64 2)))
(.f64 (cbrt.f64 (/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (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 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))) (/.f64 (cbrt.f64 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)) (cbrt.f64 2)))
(*.f64 (/.f64 (cos.f64 th) (/.f64 1 a2)) (/.f64 a2 (sqrt.f64 2)))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a2)) (/.f64 a2 (pow.f64 2 1/4)))
(pow.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) a2)) 2)
(pow.f64 (*.f64 a2 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))) 2)
(*.f64 (/.f64 a2 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (/.f64 (pow.f64 2 1/4) a2)))
(pow.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) a2)) 2)
(pow.f64 (*.f64 a2 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))) 2)
(*.f64 (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) a2)) (/.f64 a2 (cbrt.f64 (sqrt.f64 2))))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a2 a2))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2)) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(.f64 (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(*.f64 (/.f64 a2 (cbrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 2) a2)))
(.f64 (/.f64 1 (cbrt.f64 2)) (/.f64 (cos.f64 th) (/.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 a2 a2))))
(*.f64 (/.f64 a2 (/.f64 (cbrt.f64 (sqrt.f64 2)) a2)) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(.f64 (/.f64 (.f64 a2 a2) (cbrt.f64 (sqrt.f64 2))) (/.f64 (cos.f64 th) (cbrt.f64 2)))
(.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 (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 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))
(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) a2)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) a2)) a2)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (sqrt.f64 (cos.f64 th)))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))) (.f64 (neg.f64 a2) a2))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 a2 (.f64 (neg.f64 a2) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
(*.f64 (/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4)))) (pow.f64 (cbrt.f64 a2) 2))
(/.f64 (*.f64 (cos.f64 th) (pow.f64 (cbrt.f64 a2) 2)) (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4))))
(/.f64 (cos.f64 th) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (pow.f64 a2 4))) (pow.f64 (cbrt.f64 a2) 2)))
(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 (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 (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 (cbrt.f64 (.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4))) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))
(.f64 (cbrt.f64 (pow.f64 (.f64 a2 (sqrt.f64 (cos.f64 th))) 4)) (/.f64 (cbrt.f64 (.f64 a2 (.f64 a2 (cos.f64 th)))) (sqrt.f64 2)))
(*.f64 (/.f64 1 (/.f64 (/.f64 (sqrt.f64 2) a2) (cos.f64 th))) a2)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) (/.f64 (sqrt.f64 2) (.f64 a2 a2))) (cbrt.f64 (cos.f64 th)))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))) 1)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(pow.f64 (/.f64 (sqrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 1/4) a2)) 2)
(pow.f64 (*.f64 a2 (/.f64 (sqrt.f64 (cos.f64 th)) (pow.f64 2 1/4))) 2)
(pow.f64 (cbrt.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))) 3)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(pow.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))) 3) 1/3)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) (cos.f64 th)) -1)
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(neg.f64 (/.f64 (cos.f64 th) (/.f64 (neg.f64 (sqrt.f64 2)) (*.f64 a2 a2))))
(.f64 (.f64 a2 (neg.f64 a2)) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2))))
(.f64 a2 (.f64 (neg.f64 a2) (/.f64 (cos.f64 th) (neg.f64 (sqrt.f64 2)))))
(.f64 a2 (/.f64 (.f64 a2 (neg.f64 (cos.f64 th))) (neg.f64 (sqrt.f64 2))))
(sqrt.f64 (/.f64 (*.f64 (pow.f64 (cos.f64 th) 2) (pow.f64 a2 4)) 2))
(sqrt.f64 (*.f64 (/.f64 (pow.f64 (cos.f64 th) 2) 2) (pow.f64 a2 4)))
(sqrt.f64 (/.f64 (pow.f64 (*.f64 a2 (sqrt.f64 (cos.f64 th))) 4) 2))
(log.f64 (exp.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(cbrt.f64 (pow.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2))) 3))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(expm1.f64 (log1p.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(exp.f64 (log.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(log1p.f64 (expm1.f64 (.f64 (cos.f64 th) (/.f64 (.f64 a2 a2) (sqrt.f64 2)))))
(.f64 a2 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) a2))
(/.f64 (.f64 a2 (.f64 a2 (cos.f64 th))) (sqrt.f64 2))
(-.f64 (exp.f64 (log1p.f64 (.f64 (cos.f64 th) (.f64 a2 a2)))) 1)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.f64 a2 (.f64 a2 (cos.f64 th)))
(pow.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) 1)
(.f64 (cos.f64 th) (.f64 a2 a2))
(.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)))

localize66.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.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)))
✓	0.7b	(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
✓	0.7b	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
✓	1.0b	(/.f64 1 (pow.f64 2 1/4))

Compiler

Compiled 70 to 43 computations (38.6% saved)

series38.0ms (0.3%)

Counts

4 → 60

Calls

15 calls:

Time	Variable		Point	Expression
31.0ms	th	@	inf	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
3.0ms	th	@	0	(/.f64 (cos.f64 th) (pow.f64 2 1/4))
1.0ms	th	@	0	(.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)))
0.0ms	a2	@	inf	(.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)))
0.0ms	th	@	inf	(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))

rewrite163.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1742×	`associate-/r*`
1454×	`associate-/l*`
386×	`add-sqr-sqrt`
370×	`*-un-lft-identity`
368×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	102
1	391	72
2	5204	72

Stop Event

1×	node limit

Counts

4 → 367

Calls

Call 1

Inputs
(/.f64 1 (pow.f64 2 1/4))
(/.f64 (cos.f64 th) (pow.f64 2 1/4))
(*.f64 (/.f64 1 (pow.f64 2 1/4)) (/.f64 (cos.f64 th) (pow.f64 2 1/4)))
(.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)))

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

simplify222.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1566×	`associate-/l/`
1424×	`associate-/r*`
1208×	`associate-r`
1078×	`associate-l`
934×	`associate-/r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	904	19961
1	2293	19345

Stop Event

1×	node limit

Counts

427 → 579

Calls

Call 1

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

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

eval672.0ms (4.7%)

Compiler: Compiled 28757 to 16955 computations (41% saved)

prune420.0ms (2.9%)

Pruning

25 alts after pruning (21 fresh and 4 done)

	Pruned	Kept	Total
New	1339	21	1360
Fresh	12	0	12
Picked	1	0	1
Done	2	4	6
Total	1354	25	1379

Error

Counts

1379 → 25

Alt Table

Click to see full alt table

Status	Error	Program
✓	24.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
	40.8b	(/.f64 (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (.f64 a2 a2)) (sqrt.f64 2))
✓	26.9b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	29.5b	(/.f64 (*.f64 (cos.f64 th) a1) (/.f64 (sqrt.f64 2) a1))
	41.2b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
▶	37.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
▶	29.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	43.2b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	29.7b	(/.f64 (cos.f64 th) (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	37.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	29.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	43.2b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	0.5b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	26.9b	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) a2)
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	37.3b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
▶	43.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
	43.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	29.6b	(.f64 (.f64 (pow.f64 2 -1/2) (cos.f64 th)) (*.f64 a1 a1))
▶	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
	26.9b	(.f64 (.f64 a2 (*.f64 a2 (cos.f64 th))) (pow.f64 2 -1/2))
	24.3b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	26.9b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a2 a2)))
▶	29.5b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))

Compiler

Compiled 570 to 425 computations (25.4% saved)

localize16.0ms (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 (sqrt.f64 1/2) (cos.f64 th))
✓	0.4b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 42 to 17 computations (59.5% saved)

series2.0ms (0%)

Counts

2 → 40

Calls

12 calls:

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

rewrite80.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`associate-*r/`
774×	`distribute-rgt-in`
724×	`distribute-lft-in`
634×	`associate-*l/`
302×	`add-sqr-sqrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	50
1	293	48
2	3807	48

Stop Event

1×	node limit

Counts

2 → 93

Calls

Call 1

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

Outputs

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

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

904×	`associate-/l*`
818×	`associate-r`
760×	`associate-l`
750×	`distribute-lft-neg-in`
746×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	7407
1	892	6851
2	5470	6685

Stop Event

1×	node limit

Counts

133 → 155

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

series2.0ms (0%)

Counts

2 → 12

Calls

6 calls:

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

rewrite56.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

66 → 69

Calls

Call 1

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

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

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (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))

rewrite54.0ms (0.4%)

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)))))))

simplify55.0ms (0.4%)

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)))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cos.f64 th) (.f64 a1 a1))
✓	0.3b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))

Compiler

Compiled 28 to 12 computations (57.1% saved)

series3.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite60.0ms (0.4%)

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	44
1	218	44
2	2568	44

Stop Event

1×	node limit

Counts

2 → 26

Calls

Call 1

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

Outputs

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

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

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1422×	`associate-*r/`
1180×	`associate-*l/`
724×	`unswap-sqr`
628×	`fma-def`
560×	`*-commutative`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1934
1	267	1926
2	1099	1852
3	3726	1816

Stop Event

1×	node limit

Counts

74 → 68

Calls

Call 1

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

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

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 2) (cos.f64 th))
✓	0.3b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))

Compiler

Compiled 27 to 15 computations (44.4% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 109

Calls

Call 1

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

Outputs

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

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

133 → 165

Calls

Call 1

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

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

eval266.0ms (1.9%)

Compiler: Compiled 13104 to 7837 computations (40.2% saved)

prune237.0ms (1.7%)

Pruning

31 alts after pruning (23 fresh and 8 done)

	Pruned	Kept	Total
New	654	13	667
Fresh	6	10	16
Picked	0	1	1
Done	1	7	8
Total	661	31	692

Error

Counts

692 → 31

Alt Table

Click to see full alt table

Status	Error	Program
▶	37.3b	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
✓	24.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
✓	26.9b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	41.2b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
✓	37.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	29.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	43.2b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	37.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	29.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	43.2b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	43.4b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	37.2b	(.f64 (pow.f64 2 -1/2) (.f64 a2 a2))
▶	0.5b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	26.9b	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) a2)
	29.5b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	37.3b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	43.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
▶	43.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	43.2b	(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
	26.9b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2))
	29.6b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1))
	55.0b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
	55.0b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	24.3b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	47.4b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
✓	29.5b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
	26.9b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
▶	43.2b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
▶	37.2b	(.f64 a2 (.f64 a2 (pow.f64 2 -1/2)))

Compiler

Compiled 634 to 479 computations (24.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
✓	0.1b	(/.f64 1 (cos.f64 th))
✓	0.2b	(/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th)))
✓	0.4b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))

Compiler

Compiled 55 to 28 computations (49.1% saved)

series3.0ms (0%)

Counts

3 → 52

Calls

15 calls:

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

rewrite105.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1544×	`associate-/r*`
1048×	`associate-/l*`
648×	`associate-/r/`
372×	`add-sqr-sqrt`
356×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	77
1	367	59
2	4951	59

Stop Event

1×	node limit

Counts

3 → 235

Calls

Call 1

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

Outputs

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

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

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1528×	`times-frac`
1200×	`associate-r`
1194×	`associate-/r*`
996×	`associate-l`
860×	`associate-/l/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	633	14381
1	1776	13799

Stop Event

1×	node limit

Counts

287 → 376

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

Outputs
(*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (*.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(fma.f64 1/24 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1)))))
(+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 4)))) (+.f64 (.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 6)))) (+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (pow.f64 th 2)))) (.f64 (sqrt.f64 1/2) (+.f64 (pow.f64 a2 2) (pow.f64 a1 2))))))
(fma.f64 1/24 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (pow.f64 th 6))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(fma.f64 1/24 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (fma.f64 -1/720 (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (pow.f64 th 6))) (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 th th))) (.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (.f64 a1 a1))))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (pow.f64 a2 2) (pow.f64 a1 2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (*.f64 a2 a2) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a1 2) (cos.f64 th))) (.f64 (sqrt.f64 1/2) (.f64 (pow.f64 a2 2) (cos.f64 th))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(sqrt.f64 1/2)
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (sqrt.f64 1/2))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (sqrt.f64 1/2))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (sqrt.f64 1/2)))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (*.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)))
(+.f64 (.f64 -1/2 (.f64 (sqrt.f64 1/2) (pow.f64 th 2))) (+.f64 (.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4))) (+.f64 (sqrt.f64 1/2) (.f64 -1/720 (.f64 (sqrt.f64 1/2) (pow.f64 th 6))))))
(fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (+.f64 (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2)) (.f64 -1/720 (*.f64 (sqrt.f64 1/2) (pow.f64 th 6)))))
(+.f64 (fma.f64 -1/2 (.f64 (sqrt.f64 1/2) (.f64 th th)) (fma.f64 1/24 (.f64 (sqrt.f64 1/2) (pow.f64 th 4)) (sqrt.f64 1/2))) (.f64 (sqrt.f64 1/2) (*.f64 (pow.f64 th 6) -1/720)))
(*.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))
1
(+.f64 (*.f64 1/2 (pow.f64 th 2)) 1)
(fma.f64 1/2 (*.f64 th th) 1)
(+.f64 (.f64 1/2 (pow.f64 th 2)) (+.f64 1 (.f64 5/24 (pow.f64 th 4))))
(+.f64 (fma.f64 1/2 (.f64 th th) 1) (.f64 (pow.f64 th 4) 5/24))
(+.f64 (.f64 61/720 (pow.f64 th 6)) (+.f64 (.f64 1/2 (pow.f64 th 2)) (+.f64 1 (*.f64 5/24 (pow.f64 th 4)))))
(fma.f64 61/720 (pow.f64 th 6) (+.f64 (fma.f64 1/2 (.f64 th th) 1) (.f64 (pow.f64 th 4) 5/24)))
(+.f64 (.f64 (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (cos.f64 th)) (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (.f64 a2 a2))))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
(+.f64 (.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (.f64 a2 a2))) (.f64 (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (cos.f64 th)))
(.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (.f64 (sqrt.f64 1/2) (cos.f64 th)))
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(.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 1/2) -1) (neg.f64 (cos.f64 th)))
(*.f64 (neg.f64 (cos.f64 th)) (/.f64 (sqrt.f64 1/2) -1))
(.f64 (/.f64 (pow.f64 2 -1/4) 1) (.f64 (/.f64 (pow.f64 2 -1/4) 1) (cos.f64 th)))
(.f64 (pow.f64 2 -1/4) (.f64 (cos.f64 th) (pow.f64 2 -1/4)))
(*.f64 (cos.f64 th) (pow.f64 2 -1/2))
(.f64 (.f64 (/.f64 (pow.f64 2 -1/4) 1) (cos.f64 th)) (pow.f64 2 -1/4))
(.f64 (pow.f64 2 -1/4) (.f64 (cos.f64 th) (pow.f64 2 -1/4)))
(*.f64 (cos.f64 th) (pow.f64 2 -1/2))
(.f64 (/.f64 (pow.f64 2 -1/4) (cbrt.f64 (pow.f64 (cos.f64 th) -2))) (.f64 (/.f64 (pow.f64 2 -1/4) 1) (cbrt.f64 (cos.f64 th))))
(.f64 (/.f64 (pow.f64 2 -1/4) (cbrt.f64 (pow.f64 (cos.f64 th) -2))) (.f64 (pow.f64 2 -1/4) (cbrt.f64 (cos.f64 th))))
(*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (pow.f64 2 -1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))))
(*.f64 (/.f64 (cbrt.f64 1/2) 1) (/.f64 (cbrt.f64 (sqrt.f64 1/2)) (/.f64 1 (cos.f64 th))))
(.f64 (cbrt.f64 1/2) (.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 1/2))))
(.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2)))
(*.f64 (/.f64 (cbrt.f64 1/2) (pow.f64 (cos.f64 th) -1/2)) (/.f64 (cbrt.f64 (sqrt.f64 1/2)) (pow.f64 (cos.f64 th) -1/2)))
(.f64 (cbrt.f64 1/2) (.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 1/2))))
(.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2)))
(.f64 (/.f64 (cbrt.f64 1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))) (cbrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))))
(.f64 (cbrt.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th))) (/.f64 (cbrt.f64 1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))))
(*.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) 1) (neg.f64 (cos.f64 th)))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 (cos.f64 th))) 1) (sqrt.f64 (cos.f64 th)))
(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 (cos.f64 th)) (sqrt.f64 (cos.f64 th))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))) 1) (cbrt.f64 (cos.f64 th)))
(.f64 (.f64 (sqrt.f64 1/2) (cbrt.f64 (cos.f64 th))) (/.f64 1 (cbrt.f64 (pow.f64 (cos.f64 th) -2))))
(*.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))))
(*.f64 (/.f64 (cbrt.f64 1/2) (/.f64 1 (cos.f64 th))) (cbrt.f64 (sqrt.f64 1/2)))
(.f64 (cbrt.f64 1/2) (.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 1/2))))
(.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2)))
(*.f64 (/.f64 (sqrt.f64 1/2) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2))) (cbrt.f64 (cos.f64 th)))
(.f64 (cbrt.f64 (cos.f64 th)) (.f64 (sqrt.f64 1/2) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(.f64 (sqrt.f64 1/2) (.f64 (cbrt.f64 (cos.f64 th)) (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(*.f64 (/.f64 1 (/.f64 (/.f64 1 (cos.f64 th)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 1/2)))
(.f64 (cbrt.f64 1/2) (.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 1/2))))
(.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (cbrt.f64 1/2)))
(.f64 (/.f64 (.f64 (sqrt.f64 1/2) (sqrt.f64 (cos.f64 th))) (sqrt.f64 -1)) (sqrt.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 -1) (sqrt.f64 (cos.f64 th)))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(.f64 (.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 -1)) (sqrt.f64 (cos.f64 th))) (sqrt.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (/.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (cos.f64 th) -2))) -1) (cbrt.f64 (neg.f64 (cos.f64 th))))
(*.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)))) (cbrt.f64 (neg.f64 (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))
(pow.f64 (/.f64 (/.f64 1 (cos.f64 th)) (sqrt.f64 1/2)) -1)
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(neg.f64 (*.f64 (sqrt.f64 1/2) (neg.f64 (cos.f64 th))))
(*.f64 (sqrt.f64 1/2) (cos.f64 th))
(sqrt.f64 (*.f64 1/2 (pow.f64 (cos.f64 th) 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/2)) (cos.f64 th)))
(*.f64 (cos.f64 th) (log.f64 (exp.f64 (sqrt.f64 1/2))))
(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 (sqrt.f64 1/2) (/.f64 (pow.f64 (/.f64 1 (cos.f64 th)) 3) 1/2)))
(cbrt.f64 (/.f64 (sqrt.f64 1/2) (/.f64 (/.f64 1 (pow.f64 (cos.f64 th) 3)) 1/2)))
(cbrt.f64 (.f64 1/2 (.f64 (sqrt.f64 1/2) (pow.f64 (cos.f64 th) 3))))
(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))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (cos.f64 th)))) 1)
(/.f64 1 (cos.f64 th))
(*.f64 1 (/.f64 1 (cos.f64 th)))
(/.f64 1 (cos.f64 th))
(*.f64 (/.f64 1 (cos.f64 th)) 1)
(/.f64 1 (cos.f64 th))
(*.f64 (pow.f64 (cos.f64 th) -1/2) (pow.f64 (cos.f64 th) -1/2))
(/.f64 1 (cos.f64 th))
(*.f64 (/.f64 1 (cbrt.f64 (cos.f64 th))) (cbrt.f64 (pow.f64 (cos.f64 th) -2)))
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (/.f64 1 (cbrt.f64 (cos.f64 th))))
(/.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (cbrt.f64 (cos.f64 th)))
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (/.f64 1 (cbrt.f64 (cos.f64 th))))
(/.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (cbrt.f64 (cos.f64 th)))
(*.f64 -1 (/.f64 -1 (cos.f64 th)))
(/.f64 1 (cos.f64 th))
(*.f64 (/.f64 -1 (cos.f64 th)) -1)
(/.f64 1 (cos.f64 th))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)) (/.f64 1 (cbrt.f64 (cos.f64 th))))
(*.f64 (/.f64 1 (cbrt.f64 (cos.f64 th))) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 3))
(*.f64 (/.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) 1) (/.f64 1 (cbrt.f64 (cos.f64 th))))
(*.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (/.f64 1 (cbrt.f64 (cos.f64 th))))
(/.f64 (cbrt.f64 (pow.f64 (cos.f64 th) -2)) (cbrt.f64 (cos.f64 th)))
(*.f64 (pow.f64 (sqrt.f64 (cos.f64 th)) -1) (pow.f64 (sqrt.f64 (cos.f64 th)) -1))
(pow.f64 (sqrt.f64 (cos.f64 th)) -2)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cos.f64 th)) 2) -1) (pow.f64 (cbrt.f64 (cos.f64 th)) -1))
(*.f64 (/.f64 1 (cbrt.f64 (cos.f64 th))) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 3))
(pow.f64 (/.f64 1 (cos.f64 th)) 1)
(/.f64 1 (cos.f64 th))
(pow.f64 (pow.f64 (cos.f64 th) -1/2) 2)
(/.f64 1 (cos.f64 th))
(pow.f64 (/.f64 1 (cbrt.f64 (cos.f64 th))) 3)
(*.f64 (/.f64 1 (cbrt.f64 (cos.f64 th))) (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 2)))
(/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 th)) 3))
(pow.f64 (pow.f64 (/.f64 1 (cos.f64 th)) 3) 1/3)
(/.f64 1 (cos.f64 th))
(pow.f64 (cos.f64 th) -1)
(/.f64 1 (cos.f64 th))
(sqrt.f64 (pow.f64 (cos.f64 th) -2))
(log.f64 (exp.f64 (/.f64 1 (cos.f64 th))))
(/.f64 1 (cos.f64 th))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (cos.f64 th)))))
(/.f64 1 (cos.f64 th))
(cbrt.f64 (pow.f64 (/.f64 1 (cos.f64 th)) 3))
(/.f64 1 (cos.f64 th))
(expm1.f64 (log1p.f64 (/.f64 1 (cos.f64 th))))
(/.f64 1 (cos.f64 th))
(exp.f64 (neg.f64 (log.f64 (cos.f64 th))))
(/.f64 1 (cos.f64 th))
(exp.f64 (*.f64 (log.f64 (cos.f64 th)) -1))
(/.f64 1 (cos.f64 th))
(exp.f64 (*.f64 (neg.f64 (log.f64 (cos.f64 th))) 1))
(/.f64 1 (cos.f64 th))
(log1p.f64 (expm1.f64 (/.f64 1 (cos.f64 th))))
(/.f64 1 (cos.f64 th))

localize38.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 10 computations (37.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1368×	`add-sqr-sqrt`
1350×	`*-un-lft-identity`
1252×	`add-cube-cbrt`
1236×	`add-cbrt-cube`
1224×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	158	17
2	1802	17

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1474×	`distribute-rgt-in`
1446×	`distribute-lft-in`
1208×	`log-prod`
754×	`associate-r`
696×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	391
1	96	391
2	364	391
3	2000	391

Stop Event

1×	node limit

Counts

23 → 14

Calls

Call 1

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

localize28.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 17 computations (19% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1458×	`add-sqr-sqrt`
1432×	`*-un-lft-identity`
1340×	`add-cube-cbrt`
1318×	`add-cbrt-cube`
1304×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	167	28
2	1902	28

Stop Event

1×	node limit

Counts

2 → 24

Calls

Call 1

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

Outputs

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

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

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1404×	`distribute-rgt-in`
1404×	`distribute-lft-in`
1268×	`associate-+r+`
1192×	`associate-+l+`
672×	`unswap-sqr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	680
1	152	680
2	630	680
3	2344	680

Stop Event

1×	node limit

Counts

48 → 29

Calls

Call 1

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

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

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 23 to 17 computations (26.1% saved)

series0.0ms (0%)

Counts

2 → 12

Calls

3 calls:

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

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1668×	`add-sqr-sqrt`
1646×	`*-un-lft-identity`
1532×	`add-cube-cbrt`
1512×	`add-cbrt-cube`
180×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	198	22
2	2302	22

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

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

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-r`
916×	`associate-l`
810×	`associate-+r+`
800×	`associate-+l+`
398×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	871
1	237	851
2	892	845
3	4098	845

Stop Event

1×	node limit

Counts

59 → 62

Calls

Call 1

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

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

localize51.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 25 to 16 computations (36% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite97.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1896×	`add-sqr-sqrt`
1870×	`*-un-lft-identity`
1746×	`add-cube-cbrt`
1728×	`add-cbrt-cube`
190×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	208	34
2	2518	34

Stop Event

1×	node limit

Counts

2 → 76

Calls

Call 1

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

Outputs

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

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

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1176×	`associate-/l*`
994×	`associate-+r-`
858×	`associate-+l-`
756×	`associate-/r*`
678×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2140
1	438	2128
2	1681	2116
3	6354	2116

Stop Event

1×	node limit

Counts

100 → 97

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

Outputs
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
(/.f64 (pow.f64 a2 2) (sqrt.f64 2))
(*.f64 a2 (/.f64 a2 (sqrt.f64 2)))
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(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(exp.f64 (.f64 (log.f64 (.f64 (sqrt.f64 2) (pow.f64 a2 -2))) 1))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 a2 -2))))
(/.f64 (sqrt.f64 2) (*.f64 a2 a2))
(*.f64 (sqrt.f64 2) (pow.f64 a2 -2))

eval325.0ms (2.3%)

Compiler: Compiled 14129 to 8709 computations (38.4% saved)

prune171.0ms (1.2%)

Pruning

36 alts after pruning (25 fresh and 11 done)

	Pruned	Kept	Total
New	671	8	679
Fresh	1	17	18
Picked	0	1	1
Done	2	10	12
Total	674	36	710

Error

Counts

710 → 36

Alt Table

Click to see full alt table

Status	Error	Program
✓	37.3b	(pow.f64 (/.f64 (sqrt.f64 2) (*.f64 a2 a2)) -1)
	37.3b	(pow.f64 (*.f64 a2 (pow.f64 2 -1/4)) 2)
	43.2b	(pow.f64 (*.f64 a1 (pow.f64 1/2 1/4)) 2)
	37.3b	(/.f64 (/.f64 1 (sqrt.f64 2)) (pow.f64 a2 -2))
✓	24.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
✓	26.9b	(/.f64 (.f64 (cos.f64 th) (.f64 a2 a2)) (sqrt.f64 2))
	41.2b	(/.f64 (.f64 a2 (+.f64 a2 (.f64 (.f64 -1/2 (.f64 th th)) a2))) (sqrt.f64 2))
✓	37.2b	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))
✓	29.5b	(/.f64 (*.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th)))
	43.2b	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
	37.2b	(/.f64 a2 (/.f64 (sqrt.f64 2) a2))
	29.5b	(/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1))
	43.2b	(/.f64 a1 (/.f64 (sqrt.f64 2) a1))
	43.4b	(/.f64 1 (/.f64 (sqrt.f64 2) (*.f64 a1 a1)))
	47.4b	(-.f64 (+.f64 1 (.f64 (sqrt.f64 1/2) (.f64 a1 a1))) 1)
	44.3b	(-.f64 (+.f64 1 (.f64 a2 (.f64 a2 (sqrt.f64 1/2)))) 1)
	29.6b	(.f64 (/.f64 (pow.f64 2 -1/2) (/.f64 1 (cos.f64 th))) (.f64 a1 a1))
	26.9b	(.f64 (/.f64 (.f64 (cos.f64 th) a2) (sqrt.f64 2)) a2)
	29.5b	(.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (cos.f64 th))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (fma.f64 a1 a1 (.f64 a2 a2)))
✓	0.5b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
	37.3b	(*.f64 (/.f64 a2 (sqrt.f64 2)) a2)
✓	43.2b	(*.f64 (/.f64 a1 (sqrt.f64 2)) a1)
✓	43.2b	(.f64 (/.f64 1 (sqrt.f64 2)) (.f64 a1 a1))
	43.2b	(.f64 (.f64 (pow.f64 2 -1/2) a1) a1)
	26.9b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a2 a2))
	29.6b	(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (*.f64 a1 a1))
	55.0b	(.f64 (sqrt.f64 (/.f64 (.f64 a1 a1) 2)) a1)
	55.0b	(*.f64 (sqrt.f64 (/.f64 a1 (/.f64 2 a1))) a1)
	24.3b	(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
	47.4b	(.f64 (sqrt.f64 1/2) (.f64 (+.f64 (.f64 -1/2 (.f64 th th)) 1) (*.f64 a1 a1)))
✓	29.5b	(.f64 (sqrt.f64 1/2) (.f64 (cos.f64 th) (*.f64 a1 a1)))
	26.9b	(.f64 (sqrt.f64 1/2) (.f64 a2 (*.f64 a2 (cos.f64 th))))
	37.2b	(.f64 (sqrt.f64 1/2) (.f64 a2 a2))
✓	43.2b	(.f64 (sqrt.f64 1/2) (.f64 a1 a1))
	37.2b	(.f64 a2 (.f64 (sqrt.f64 1/2) a2))

Compiler

Compiled 417 to 321 computations (23% saved)

regimes217.0ms (1.5%)

Counts

63 → 1

Calls

Call 1

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

Calls

8 calls:

29.0ms	th
29.0ms	a1
28.0ms	a2
27.0ms	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
26.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 693 to 373 computations (46.2% saved)

regimes195.0ms (1.4%)

Counts

56 → 1

Calls

Call 1

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

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

Calls

7 calls:

37.0ms	a1
28.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
26.0ms	a2
26.0ms	th
23.0ms	(cos.f64 th)

Results

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

Compiler

Compiled 554 to 302 computations (45.5% saved)

regimes161.0ms (1.1%)

Counts

54 → 1

Calls

Call 1

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

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

Calls

7 calls:

26.0ms	a2
25.0ms	a1
24.0ms	th
20.0ms	(cos.f64 th)
19.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Results

Error	Segments	Branch
0.4b	1	`a1`
0.4b	1	`a2`
0.4b	1	`th`
0.4b	1	`(/.f64 (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 530 to 293 computations (44.7% saved)

regimes546.0ms (3.8%)

Counts

50 → 4

Calls

Call 1

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

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

Calls

7 calls:

128.0ms	a1
100.0ms	th
65.0ms	a2
64.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
60.0ms	(cos.f64 th)

Results

Error	Segments	Branch
7.6b	4	`a1`
8.4b	2	`a2`
9.5b	5	`th`
9.7b	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.7b	4	`(cos.f64 th)`
10.9b	4	`(*.f64 a1 a1)`
11.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 474 to 273 computations (42.4% saved)

bsearch142.0ms (1%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
39.0ms	-1.805337107090721e-155	-7.134441151527986e-162
22.0ms	-6.258043598872805e-96	-2.408608572773361e-96
80.0ms	-2.5054099675153184e-58	-3.4339222387249844e-61

Results

88.0ms	91×	body	1024	valid
39.0ms	230×	body	256	valid
10.0ms	31×	body	512	valid

Compiler

Compiled 613 to 460 computations (25% saved)

regimes609.0ms (4.2%)

Counts

42 → 4

Calls

Call 1

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

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

Calls

7 calls:

116.0ms	th
103.0ms	a2
101.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
92.0ms	(*.f64 a2 a2)
69.0ms	a1

Results

Error	Segments	Branch
7.6b	4	`a1`
8.4b	2	`a2`
9.5b	5	`th`
9.7b	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.7b	4	`(cos.f64 th)`
10.9b	4	`(*.f64 a1 a1)`
11.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 397 to 237 computations (40.3% saved)

bsearch145.0ms (1%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
54.0ms	-1.805337107090721e-155	-7.134441151527986e-162
23.0ms	-6.258043598872805e-96	-2.408608572773361e-96
68.0ms	-2.5054099675153184e-58	-3.4339222387249844e-61

Results

55.0ms	236×	body	256	valid
42.0ms	83×	body	1024	valid
41.0ms	33×	body	512	valid

Compiler

Compiled 613 to 460 computations (25% saved)

regimes432.0ms (3%)

Counts

40 → 4

Calls

Call 1

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

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

Calls

7 calls:

88.0ms	th
71.0ms	a1
55.0ms	(*.f64 a1 a1)
54.0ms	(cos.f64 th)
53.0ms	a2

Results

Error	Segments	Branch
7.6b	4	`a1`
8.4b	2	`a2`
9.5b	5	`th`
9.7b	4	`(/.f64 (cos.f64 th) (sqrt.f64 2))`
9.7b	4	`(cos.f64 th)`
10.9b	4	`(*.f64 a1 a1)`
11.3b	4	`(*.f64 a2 a2)`

Compiler

Compiled 379 to 228 computations (39.8% saved)

bsearch103.0ms (0.7%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
40.0ms	-1.805337107090721e-155	-7.134441151527986e-162
21.0ms	-6.258043598872805e-96	-2.408608572773361e-96
41.0ms	-2.5054099675153184e-58	-3.4339222387249844e-61

Results

48.0ms	99×	body	1024	valid
36.0ms	208×	body	256	valid
13.0ms	45×	body	512	valid

Compiler

Compiled 613 to 460 computations (25% saved)

regimes184.0ms (1.3%)

Counts

29 → 3

Calls

Call 1

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

Calls

6 calls:

50.0ms	th
30.0ms	(*.f64 a2 a2)
27.0ms	a1
25.0ms	a2
24.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
17.3b	2	`a1`
17.2b	2	`a2`
15.3b	3	`th`
15.3b	2	`(cos.f64 th)`
19.0b	2	`(*.f64 a1 a1)`
18.6b	2	`(*.f64 a2 a2)`

Compiler

Compiled 272 to 174 computations (36% saved)

bsearch53.0ms (0.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
26.0ms	3522747687314124000.0	4.774864383850556e+27
26.0ms	-0.0010160666453072865	-7.995153618479798e-10

Results

48.0ms

288×

body

256

valid

Compiler

Compiled 514 to 380 computations (26.1% saved)

regimes66.0ms (0.5%)

Counts

28 → 1

Calls

Call 1

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

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

Calls

5 calls:

14.0ms	a2
13.0ms	a1
13.0ms	th
10.0ms	(*.f64 a2 a2)
9.0ms	(*.f64 a1 a1)

Results

Error	Segments	Branch
24.2b	1	`a1`
24.2b	1	`a2`
24.2b	1	`th`
24.2b	1	`(*.f64 a1 a1)`
24.2b	1	`(*.f64 a2 a2)`

Compiler

Compiled 258 to 164 computations (36.4% saved)

regimes48.0ms (0.3%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	a1
10.0ms	a2
9.0ms	th
8.0ms	(*.f64 a2 a2)
6.0ms	(*.f64 a1 a1)

Results

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

Compiler

Compiled 164 to 106 computations (35.4% saved)

regimes77.0ms (0.5%)

Counts

16 → 2

Calls

Call 1

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

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

Calls

5 calls:

19.0ms	(*.f64 a1 a1)
17.0ms	a2
15.0ms	a1
10.0ms	(*.f64 a2 a2)
10.0ms	th

Results

Error	Segments	Branch
27.8b	2	`a1`
28.2b	2	`a2`
37.2b	1	`th`
28.4b	4	`(*.f64 a1 a1)`
30.5b	2	`(*.f64 a2 a2)`

Compiler

Compiled 134 to 87 computations (35.1% saved)

bsearch33.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
33.0ms	-9.997030051789823e-50	-1.4989206726516512e-51

Results

16.0ms	31×	body	1024	valid
10.0ms	65×	body	256	valid
5.0ms	16×	body	512	valid

Compiler

Compiled 168 to 132 computations (21.4% saved)

regimes45.0ms (0.3%)

Counts

6 → 2

Calls

Call 1

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

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

Calls

5 calls:

13.0ms	(*.f64 a1 a1)
10.0ms	a1
9.0ms	a2
8.0ms	(*.f64 a2 a2)
4.0ms	th

Results

Error	Segments	Branch
27.9b	2	`a1`
28.2b	2	`a2`
37.2b	1	`th`
28.4b	4	`(*.f64 a1 a1)`
30.5b	2	`(*.f64 a2 a2)`

Compiler

Compiled 63 to 44 computations (30.2% saved)

bsearch30.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
30.0ms	-9.997030051789823e-50	-1.4989206726516512e-51

Results

15.0ms	29×	body	1024	valid
12.0ms	77×	body	256	valid
2.0ms	6×	body	512	valid

Compiler

Compiled 168 to 132 computations (21.4% saved)

regimes33.0ms (0.2%)

Accuracy

Total -27.9b remaining (-100.1%)

Threshold costs -27.9b (-100.1%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	(*.f64 a1 a1)
7.0ms	a1
6.0ms	a2
5.0ms	(*.f64 a2 a2)
4.0ms	th

Results

Error	Segments	Branch
27.9b	2	`a1`
28.2b	2	`a2`
37.2b	1	`th`
28.4b	4	`(*.f64 a1 a1)`
30.5b	2	`(*.f64 a2 a2)`

Compiler

Compiled 45 to 32 computations (28.9% saved)

bsearch29.0ms (0.2%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
28.0ms	-9.997030051789823e-50	-1.4989206726516512e-51

Results

13.0ms	29×	body	1024	valid
12.0ms	77×	body	256	valid
2.0ms	6×	body	512	valid

Compiler

Compiled 168 to 132 computations (21.4% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative`
2×	`+-commutative`
2×	`if-if-or-not`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	805
1	95	805

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(if (<=.f64 a1 -1696173182187249/226156424291633194186662080095093570025917938800079226639565593765455331328) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (if (<=.f64 a1 -8657667377137459/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1)) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a1 -6643344963566725/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -2404907604760405/601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1)) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a1 -5427754182999197/113078212145816597093331040047546785012958969400039613319782796882727665664) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -6733741293329135/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (.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 -8116567392432203/18446744073709551616) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 th 3600000000000000000) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(if (<=.f64 a1 -5054990000090745/1684996666696914987166688442938726917102321526408785780068975640576) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -4380991333411979/842498333348457493583344221469363458551160763204392890034487820288) (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -8214358750147461/210624583337114373395836055367340864637790190801098222508621955072) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))

Outputs
(/.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
(.f64 (.f64 (sqrt.f64 1/2) (cos.f64 th)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(.f64 (.f64 (cos.f64 th) (sqrt.f64 1/2)) (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
(if (<=.f64 a1 -1696173182187249/226156424291633194186662080095093570025917938800079226639565593765455331328) (/.f64 (.f64 a1 a1) (/.f64 (sqrt.f64 2) (cos.f64 th))) (if (<=.f64 a1 -8657667377137459/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1)) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a1 -6643344963566725/28269553036454149273332760011886696253239742350009903329945699220681916416) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -2404907604760405/601226901190101306339707032778070279008174732520529886901066488712245510429339761526706943586500787976175353856) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (/.f64 a1 (/.f64 (/.f64 (sqrt.f64 2) (cos.f64 th)) a1)) (*.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))))))
(if (<=.f64 a1 -5427754182999197/113078212145816597093331040047546785012958969400039613319782796882727665664) (.f64 (cos.f64 th) (/.f64 (.f64 a1 a1) (sqrt.f64 2))) (if (<=.f64 a1 -6733741293329135/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (if (<=.f64 a1 -8695209426788831/483067190377157293086918986366498418037365916213304374832154406431439892786195053067024220822740322245307952003937772147170634832630373456967863584183385093587122601852928) (.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 -8116567392432203/18446744073709551616) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (if (<=.f64 th 3600000000000000000) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2)) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))))
(if (or (<=.f64 th -8116567392432203/18446744073709551616) (not (<=.f64 th 3600000000000000000))) (.f64 (cos.f64 th) (/.f64 a2 (/.f64 (sqrt.f64 2) a2))) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a2 a2) (*.f64 a1 a1)))
(.f64 (sqrt.f64 1/2) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
(if (<=.f64 a1 -5054990000090745/1684996666696914987166688442938726917102321526408785780068975640576) (*.f64 (/.f64 a1 (sqrt.f64 2)) a1) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -5054990000090745/1684996666696914987166688442938726917102321526408785780068975640576) (*.f64 a1 (/.f64 a1 (sqrt.f64 2))) (/.f64 a2 (/.f64 (sqrt.f64 2) a2)))
(if (<=.f64 a1 -4380991333411979/842498333348457493583344221469363458551160763204392890034487820288) (.f64 (/.f64 a1 (sqrt.f64 2)) a1) (.f64 a2 (*.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -4380991333411979/842498333348457493583344221469363458551160763204392890034487820288) (.f64 a1 (/.f64 a1 (sqrt.f64 2))) (.f64 a2 (*.f64 a2 (sqrt.f64 1/2))))
(if (<=.f64 a1 -8214358750147461/210624583337114373395836055367340864637790190801098222508621955072) (.f64 (sqrt.f64 1/2) (.f64 a1 a1)) (.f64 a2 (.f64 (sqrt.f64 1/2) a2)))
(if (<=.f64 a1 -8214358750147461/210624583337114373395836055367340864637790190801098222508621955072) (.f64 (.f64 a1 a1) (sqrt.f64 1/2)) (.f64 a2 (.f64 a2 (sqrt.f64 1/2))))
(.f64 a2 (.f64 (sqrt.f64 1/2) a2))
(.f64 a2 (.f64 a2 (sqrt.f64 1/2)))

Compiler

Compiled 325 to 218 computations (32.9% saved)

soundness100.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

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

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
0	517	11182
1	1295	10634
2	6582	10454

Stop Event

1×	node limit
1×	saturated

Compiler

Compiled 140 to 74 computations (47.1% saved)

end129.0ms (0.9%)

Compiler: Compiled 319 to 175 computations (45.1% 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