Details

analyze1.7s (13.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample7.7s (62.8%)

Results

5.8s	4680×	body	1024	valid
1.2s	1556×	body	512	valid
364.0ms	1466×	body	128	valid
269.0ms	540×	body	256	valid
38.0ms	14×	body	2048	valid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess38.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

739×	`associate-/r/_binary64`
592×	`associate-*r/_binary64`
430×	`associate-l_binary64`
352×	`associate-r_binary64`
348×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	104
1	54	72
2	114	72
3	221	72
4	648	72
5	2866	72
6	4530	72
0	3	3

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 kx))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 th) 2)))) (sin.f64 ky))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 kx))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 th) 2)))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sin.f64 kx) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 ky) (sin.f64 th))))
(*.f64 (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 th) 2)))) (sin.f64 ky))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 th) 2)))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 th))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 th)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 th))))

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-l_binary64`
330×	`sqr-pow_binary64`
320×	`*-commutative_binary64`
275×	`associate-/r/_binary64`
269×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	18
2	51	18
3	79	18
4	160	18
5	450	18
6	1702	18
7	3048	18
8	3896	18
9	4149	18
10	4488	18
11	4978	18

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

1.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	3.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
✓	3.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series28.0ms (0.2%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
4.0ms	kx	@	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
3.0ms	ky	@	0	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
3.0ms	ky	@	inf	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	th	@	-inf	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	kx	@	inf	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

373×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
173×	`log-pow_binary64`
149×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	210	34
2	2890	34

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (sin.f64 ky) (sin.f64 th))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))

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

Outputs

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

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

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

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
213×	`associate-/r/_binary64`
186×	`fma-neg_binary64`
168×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	2472
1	637	2312
2	2395	2085

Stop Event

1×	node limit

Counts

166 → 139

Calls

Call 1

Inputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 5))))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 5) (sin.f64 ky))))) (+.f64 (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 7) (sin.f64 ky)))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 th) ky)
(-.f64 (.f64 (sin.f64 th) ky) (.f64 1/6 (*.f64 (sin.f64 th) (pow.f64 ky 3))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5))) (.f64 (sin.f64 th) ky)) (.f64 1/6 (*.f64 (sin.f64 th) (pow.f64 ky 3))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5))) (.f64 (sin.f64 th) ky)) (+.f64 (.f64 1/6 (.f64 (sin.f64 th) (pow.f64 ky 3))) (.f64 1/5040 (*.f64 (sin.f64 th) (pow.f64 ky 7)))))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) th)
(-.f64 (.f64 th (sin.f64 ky)) (.f64 1/6 (*.f64 (pow.f64 th 3) (sin.f64 ky))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 th 5) (sin.f64 ky))) (.f64 th (sin.f64 ky))) (.f64 1/6 (*.f64 (pow.f64 th 3) (sin.f64 ky))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 th 5) (sin.f64 ky))) (.f64 th (sin.f64 ky))) (+.f64 (.f64 1/6 (.f64 (pow.f64 th 3) (sin.f64 ky))) (.f64 1/5040 (*.f64 (pow.f64 th 7) (sin.f64 ky)))))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 kx)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (sin.f64 kx))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (sin.f64 kx)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3))) (*.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 5))) (+.f64 (sin.f64 kx) (+.f64 (.f64 1/45 (/.f64 (pow.f64 ky 6) (sin.f64 kx))) (.f64 1/12 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 3))))))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx))) (.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sin.f64 ky)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (sin.f64 ky))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (sin.f64 ky)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3))) (*.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (+.f64 (.f64 1/45 (/.f64 (pow.f64 kx 6) (sin.f64 ky))) (+.f64 (.f64 1/12 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 3))) (sin.f64 ky))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3))) (.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Outputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (/.f64 (.f64 (pow.f64 ky 3) (*.f64 (sin.f64 th) 1/6)) (sin.f64 kx))))
(-.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (-.f64 (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/120 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 5))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/120 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 5))) (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (/.f64 (.f64 (pow.f64 ky 3) (*.f64 (sin.f64 th) 1/6)) (sin.f64 kx))))
(fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky (-.f64 (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (.f64 (.f64 (/.f64 (pow.f64 ky 5) (sin.f64 kx)) (sin.f64 th)) (+.f64 (/.f64 1/4 (pow.f64 (sin.f64 kx) 2)) 1/120))) (.f64 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(-.f64 (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 1/120 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 5))))))) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 7) (pow.f64 ky 7))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 7))) (fma.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3)) (/.f64 (.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) 1/5040) (sin.f64 kx))))))))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
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(-.f64 (fma.f64 1/120 (.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 5))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 th (sin.f64 ky)))) (fma.f64 1/6 (.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 3))) (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 7))))))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (sin.f64 th) (/.f64 (.f64 1/2 (.f64 (sin.f64 th) (*.f64 kx kx))) (pow.f64 (sin.f64 ky) 2)))
(+.f64 (sin.f64 th) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))))
(fma.f64 (.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) 2)) (sin.f64 th)) -1/2 (sin.f64 th))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4)))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 kx kx)))))
(+.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4))) (sin.f64 th))) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 kx kx))))
(fma.f64 (.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) 2)) (sin.f64 th)) -1/2 (+.f64 (sin.f64 th) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (+.f64 (/.f64 3/8 (pow.f64 (sin.f64 ky) 2)) 1/6))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4)))))) (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 6))) (fma.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6)) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))) (.f64 1/45 (/.f64 (*.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4))) (sin.f64 th))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 4)) (pow.f64 kx 6)) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 6)) (pow.f64 kx 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 1/45 (/.f64 (pow.f64 kx 6) (/.f64 (pow.f64 (sin.f64 ky) 2) (sin.f64 th))))))))
(-.f64 (+.f64 (sin.f64 th) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (+.f64 (/.f64 3/8 (pow.f64 (sin.f64 ky) 2)) 1/6))) (+.f64 (fma.f64 1/2 (.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) 2)) (sin.f64 th)) (.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 6)) (pow.f64 kx 6)))) (.f64 (.f64 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 2)) (sin.f64 th)) (+.f64 1/45 (/.f64 1/4 (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(*.f64 (sin.f64 th) ky)
(-.f64 (.f64 (sin.f64 th) ky) (.f64 1/6 (*.f64 (sin.f64 th) (pow.f64 ky 3))))
(-.f64 (.f64 (sin.f64 th) ky) (.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) 1/6))
(fma.f64 (sin.f64 th) ky (.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) -1/6))
(.f64 (sin.f64 th) (-.f64 ky (.f64 (pow.f64 ky 3) 1/6)))
(-.f64 (+.f64 (.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5))) (.f64 (sin.f64 th) ky)) (.f64 1/6 (*.f64 (sin.f64 th) (pow.f64 ky 3))))
(+.f64 (fma.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5)) (.f64 (sin.f64 th) ky)) (.f64 -1/6 (.f64 (sin.f64 th) (pow.f64 ky 3))))
(fma.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) 1/120 (fma.f64 (sin.f64 th) ky (.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) -1/6)))
(fma.f64 (sin.f64 th) (.f64 (pow.f64 ky 5) 1/120) (.f64 (sin.f64 th) (-.f64 ky (*.f64 (pow.f64 ky 3) 1/6))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5))) (.f64 (sin.f64 th) ky)) (+.f64 (.f64 1/6 (.f64 (sin.f64 th) (pow.f64 ky 3))) (.f64 1/5040 (*.f64 (sin.f64 th) (pow.f64 ky 7)))))
(-.f64 (fma.f64 1/120 (.f64 (sin.f64 th) (pow.f64 ky 5)) (.f64 (sin.f64 th) ky)) (fma.f64 1/6 (.f64 (sin.f64 th) (pow.f64 ky 3)) (.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) 1/5040)))
(+.f64 (fma.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) 1/120 (fma.f64 (sin.f64 th) ky (.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) -1/6))) (.f64 -1/5040 (*.f64 (sin.f64 th) (pow.f64 ky 7))))
(+.f64 (.f64 (sin.f64 th) (+.f64 ky (.f64 1/120 (pow.f64 ky 5)))) (.f64 (sin.f64 th) (-.f64 (.f64 -1/6 (pow.f64 ky 3)) (*.f64 1/5040 (pow.f64 ky 7)))))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 ky) th)
(*.f64 th (sin.f64 ky))
(-.f64 (.f64 th (sin.f64 ky)) (.f64 1/6 (*.f64 (pow.f64 th 3) (sin.f64 ky))))
(+.f64 (.f64 th (sin.f64 ky)) (.f64 -1/6 (*.f64 (sin.f64 ky) (pow.f64 th 3))))
(.f64 (sin.f64 ky) (-.f64 th (.f64 1/6 (pow.f64 th 3))))
(.f64 (sin.f64 ky) (+.f64 th (.f64 (pow.f64 th 3) -1/6)))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 th 5) (sin.f64 ky))) (.f64 th (sin.f64 ky))) (.f64 1/6 (*.f64 (pow.f64 th 3) (sin.f64 ky))))
(+.f64 (fma.f64 1/120 (.f64 (sin.f64 ky) (pow.f64 th 5)) (.f64 th (sin.f64 ky))) (.f64 -1/6 (.f64 (sin.f64 ky) (pow.f64 th 3))))
(fma.f64 1/120 (.f64 (sin.f64 ky) (pow.f64 th 5)) (.f64 (sin.f64 ky) (-.f64 th (*.f64 1/6 (pow.f64 th 3)))))
(.f64 (sin.f64 ky) (-.f64 (fma.f64 1/120 (pow.f64 th 5) th) (.f64 1/6 (pow.f64 th 3))))
(-.f64 (+.f64 (.f64 1/120 (.f64 (pow.f64 th 5) (sin.f64 ky))) (.f64 th (sin.f64 ky))) (+.f64 (.f64 1/6 (.f64 (pow.f64 th 3) (sin.f64 ky))) (.f64 1/5040 (*.f64 (pow.f64 th 7) (sin.f64 ky)))))
(-.f64 (fma.f64 1/120 (.f64 (sin.f64 ky) (pow.f64 th 5)) (.f64 th (sin.f64 ky))) (fma.f64 1/6 (.f64 (sin.f64 ky) (pow.f64 th 3)) (.f64 1/5040 (*.f64 (sin.f64 ky) (pow.f64 th 7)))))
(-.f64 (.f64 (sin.f64 ky) (+.f64 th (.f64 1/120 (pow.f64 th 5)))) (.f64 (sin.f64 ky) (+.f64 (.f64 1/6 (pow.f64 th 3)) (*.f64 1/5040 (pow.f64 th 7)))))
(.f64 (sin.f64 ky) (-.f64 (fma.f64 1/120 (pow.f64 th 5) th) (fma.f64 1/6 (pow.f64 th 3) (.f64 1/5040 (pow.f64 th 7)))))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 kx)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (sin.f64 kx))
(fma.f64 1/2 (/.f64 (*.f64 ky ky) (sin.f64 kx)) (sin.f64 kx))
(fma.f64 1/2 (/.f64 ky (/.f64 (sin.f64 kx) ky)) (sin.f64 kx))
(fma.f64 1/2 (*.f64 (/.f64 ky (sin.f64 kx)) ky) (sin.f64 kx))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (sin.f64 kx)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3))) (*.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)) (sin.f64 kx)) (fma.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx)) (.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)))))
(-.f64 (fma.f64 1/2 (/.f64 ky (/.f64 (sin.f64 kx) ky)) (sin.f64 kx)) (fma.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)) (/.f64 1/6 (/.f64 (sin.f64 kx) (pow.f64 ky 4)))))
(-.f64 (fma.f64 1/2 (.f64 (/.f64 ky (sin.f64 kx)) ky) (sin.f64 kx)) (.f64 (/.f64 (pow.f64 ky 4) (sin.f64 kx)) (+.f64 (/.f64 1/8 (pow.f64 (sin.f64 kx) 2)) 1/6)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (sin.f64 kx))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 5))) (+.f64 (sin.f64 kx) (+.f64 (.f64 1/45 (/.f64 (pow.f64 ky 6) (sin.f64 kx))) (.f64 1/12 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 3))))))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx))) (.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)) (fma.f64 1/16 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 5)) (+.f64 (sin.f64 kx) (fma.f64 1/45 (/.f64 (pow.f64 ky 6) (sin.f64 kx)) (.f64 1/12 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 3))))))) (fma.f64 1/6 (/.f64 (pow.f64 ky 4) (sin.f64 kx)) (*.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)))))
(-.f64 (fma.f64 1/2 (/.f64 ky (/.f64 (sin.f64 kx) ky)) (+.f64 (fma.f64 1/45 (/.f64 (pow.f64 ky 6) (sin.f64 kx)) (*.f64 1/12 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 3)))) (fma.f64 1/16 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 5)) (sin.f64 kx)))) (fma.f64 1/8 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)) (/.f64 1/6 (/.f64 (sin.f64 kx) (pow.f64 ky 4)))))
(-.f64 (+.f64 (fma.f64 1/2 (.f64 (/.f64 ky (sin.f64 kx)) ky) (fma.f64 1/16 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 5)) (sin.f64 kx))) (.f64 (/.f64 (pow.f64 ky 6) (sin.f64 kx)) (+.f64 1/45 (/.f64 1/12 (pow.f64 (sin.f64 kx) 2))))) (*.f64 (/.f64 (pow.f64 ky 4) (sin.f64 kx)) (+.f64 (/.f64 1/8 (pow.f64 (sin.f64 kx) 2)) 1/6)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 ky)
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (sin.f64 ky))
(fma.f64 1/2 (/.f64 (*.f64 kx kx) (sin.f64 ky)) (sin.f64 ky))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (sin.f64 ky)) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3))) (*.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)) (sin.f64 ky)) (fma.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3)) (.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(-.f64 (fma.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)) (sin.f64 ky)) (.f64 (/.f64 (pow.f64 kx 4) (sin.f64 ky)) (+.f64 (/.f64 1/8 (pow.f64 (sin.f64 ky) 2)) 1/6)))
(-.f64 (+.f64 (.f64 1/16 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 5))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (sin.f64 ky))) (+.f64 (.f64 1/45 (/.f64 (pow.f64 kx 6) (sin.f64 ky))) (+.f64 (.f64 1/12 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 3))) (sin.f64 ky))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3))) (.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 5)) (fma.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)) (fma.f64 1/45 (/.f64 (pow.f64 kx 6) (sin.f64 ky)) (fma.f64 1/12 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 3)) (sin.f64 ky))))) (fma.f64 1/8 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 3)) (.f64 1/6 (/.f64 (pow.f64 kx 4) (sin.f64 ky)))))
(-.f64 (fma.f64 1/16 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 5)) (+.f64 (.f64 (/.f64 (pow.f64 kx 6) (sin.f64 ky)) (+.f64 1/45 (/.f64 1/12 (pow.f64 (sin.f64 ky) 2)))) (fma.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)) (sin.f64 ky)))) (*.f64 (/.f64 (pow.f64 kx 4) (sin.f64 ky)) (+.f64 (/.f64 1/8 (pow.f64 (sin.f64 ky) 2)) 1/6)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

prune163.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

0.0b

Counts

141 → 9

Alt Table

Status	Error	Program
	3.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
	13.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (-.f64 (exp.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 1))
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	3.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
	0.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	0.5b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 3572 to 1568 computations (56.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series14.0ms (0.1%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	kx	@	-inf	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	kx	@	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	ky	@	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	th	@	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	th	@	-inf	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
176×	`prod-diff_binary64`
174×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	248	31
2	2862	31

Stop Event

1×	node limit

Counts

2 → 84

Calls

Call 1

Inputs
(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

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

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

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
368×	`associate-/r/_binary64`
177×	`fma-neg_binary64`
174×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2908
1	628	2884
2	2493	2627

Stop Event

1×	node limit

Counts

156 → 133

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th)
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/6 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5)))) (.f64 1/6 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5)))) (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))) (.f64 1/5040 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 7)))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(/.f64 (sin.f64 th) (sin.f64 kx))
(-.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 7)))))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(/.f64 (sin.f64 th) (sin.f64 ky))
(-.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (+.f64 (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 7)))))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 5))))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 5) (sin.f64 ky))))) (+.f64 (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 7) (sin.f64 ky)))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))

Outputs
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th)
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th)
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/6 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th) (.f64 -1/6 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 3))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (.f64 (.f64 -1/6 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))) (pow.f64 th 3)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (-.f64 th (.f64 1/6 (pow.f64 th 3))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5)))) (.f64 1/6 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))))
(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 5)))) (.f64 -1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 3))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (fma.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 5)) (.f64 (*.f64 -1/6 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))) (pow.f64 th 3))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (-.f64 (.f64 1/120 (pow.f64 th 5)) (*.f64 1/6 (pow.f64 th 3)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) th) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5)))) (+.f64 (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 3))) (.f64 1/5040 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 7)))))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 5)))) (fma.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 3)) (.f64 1/5040 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 7)))))
(-.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) th (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (pow.f64 th 5) 1/120))) (fma.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (pow.f64 th 7)) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (*.f64 (pow.f64 th 3) 1/6))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (+.f64 th (.f64 1/120 (pow.f64 th 5)))) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (-.f64 (.f64 -1/6 (pow.f64 th 3)) (*.f64 1/5040 (pow.f64 th 7)))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(/.f64 (sin.f64 th) (sin.f64 kx))
(-.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))))
(+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (.f64 ky ky)))))
(+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (/.f64 (.f64 ky (*.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) -1/2))
(fma.f64 (/.f64 (.f64 ky (.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) -1/2 (/.f64 (sin.f64 th) (sin.f64 kx)))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))))
(+.f64 (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 4))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (.f64 ky ky)))))
(+.f64 (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 4)) (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 4))) (/.f64 (sin.f64 th) (sin.f64 kx)))) (.f64 (/.f64 (.f64 ky (.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) -1/2))
(fma.f64 (/.f64 (.f64 ky (.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) -1/2 (fma.f64 1/6 (.f64 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)) (sin.f64 th)) (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 4)) (/.f64 (sin.f64 th) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 3))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 7)))))))
(-.f64 (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 4))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 4)) (pow.f64 (sin.f64 kx) 3))))) (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/45 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 6))) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (.f64 ky ky))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 6)) (pow.f64 (sin.f64 kx) 7)))))))
(-.f64 (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 4)) (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 4))) (/.f64 (sin.f64 th) (sin.f64 kx)))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 6)) (fma.f64 1/45 (/.f64 (pow.f64 ky 6) (/.f64 (pow.f64 (sin.f64 kx) 3) (sin.f64 th))) (fma.f64 1/2 (/.f64 (.f64 ky (.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) (.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 6)))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (pow.f64 ky 4) (pow.f64 (sin.f64 kx) 3)) (sin.f64 th)) (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 4)) (/.f64 (sin.f64 th) (sin.f64 kx)))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 5)) (pow.f64 ky 6)) (fma.f64 1/2 (/.f64 (.f64 ky (.f64 ky (sin.f64 th))) (pow.f64 (sin.f64 kx) 3)) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 6)) (.f64 1/45 (.f64 (/.f64 (pow.f64 ky 6) (pow.f64 (sin.f64 kx) 3)) (sin.f64 th)))))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (sin.f64 th))
(/.f64 (sin.f64 th) (sin.f64 ky))
(-.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))))
(+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 3) (.f64 kx kx)))))
(+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (*.f64 kx kx)) -1/2))
(fma.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (.f64 kx kx)) -1/2 (/.f64 (sin.f64 th) (sin.f64 ky)))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))))
(+.f64 (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 5) (pow.f64 kx 4))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 3) (.f64 kx kx)))))
(+.f64 (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 4)) (/.f64 (sin.f64 th) (sin.f64 ky)))) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (*.f64 kx kx)) -1/2))
(fma.f64 3/8 (.f64 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 5)) (sin.f64 th)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 4)) (fma.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (.f64 kx kx)) -1/2 (/.f64 (sin.f64 th) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (+.f64 (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 3))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 3))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 7)))))))
(-.f64 (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 5) (pow.f64 kx 4))) (+.f64 (/.f64 (sin.f64 th) (sin.f64 ky)) (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 3))))) (fma.f64 1/45 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 3) (pow.f64 kx 6))) (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 5)) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 3) (.f64 kx kx))) (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 7)))))))
(-.f64 (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 5)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 4)) (/.f64 (sin.f64 th) (sin.f64 ky)))) (fma.f64 1/45 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 6)) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 5)) (pow.f64 kx 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (.f64 kx kx)) (.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 7)) (pow.f64 kx 6)))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 4)) (fma.f64 3/8 (.f64 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 5)) (sin.f64 th)) (/.f64 (sin.f64 th) (sin.f64 ky)))) (fma.f64 1/45 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (pow.f64 kx 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)) (.f64 kx kx)) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 7)) (pow.f64 kx 6)) (/.f64 (.f64 1/4 (.f64 (sin.f64 th) (pow.f64 kx 6))) (pow.f64 (sin.f64 ky) 5))))))
(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (sin.f64 th) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(+.f64 (sin.f64 th) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (*.f64 kx kx)) -1/2))
(fma.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) -1/2 (sin.f64 th))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4)))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (*.f64 kx kx)))))
(+.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4))) (sin.f64 th))) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) -1/2))
(fma.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) -1/2 (+.f64 (sin.f64 th) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (+.f64 (/.f64 3/8 (pow.f64 (sin.f64 ky) 2)) 1/6))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4)))))) (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 6))) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))) (*.f64 1/45 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 6))))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 4))) (sin.f64 th))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 4)) (pow.f64 kx 6)) (fma.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 1/45 (*.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 6)))))))
(-.f64 (+.f64 (sin.f64 th) (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (+.f64 (/.f64 3/8 (pow.f64 (sin.f64 ky) 2)) 1/6))) (+.f64 (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 5/16 (.f64 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 6)) (sin.f64 th)))) (.f64 (.f64 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 2)) (sin.f64 th)) (+.f64 1/45 (/.f64 1/4 (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (sin.f64 th)))

prune169.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	168	9	177

Error

Counts

177 → 9

Alt Table

Status	Error	Program
	3.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	8.1b	(*.f64 (/.f64 (sin.f64 ky) 1) (log1p.f64 (expm1.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	31.3b	(.f64 (/.f64 (sin.f64 ky) 1) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (cbrt.f64 (exp.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))))
	13.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (-.f64 (exp.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 1))
	3.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
	0.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 4788 to 2290 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

series15.0ms (0.1%)

Counts

2 → 72

Calls

18 calls:

Time	Variable		Point	Expression
4.0ms	ky	@	inf	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
2.0ms	kx	@	0	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
1.0ms	ky	@	0	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
1.0ms	th	@	0	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
1.0ms	th	@	-inf	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

571×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
173×	`log-pow_binary64`
171×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	209	31
2	2834	31

Stop Event

1×	node limit

Counts

2 → 82

Calls

Call 1

Inputs
(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

Outputs

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

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

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-def_binary64`
382×	`cancel-sign-sub-inv_binary64`
232×	`associate-/r/_binary64`
138×	`fma-neg_binary64`
136×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2827
1	642	2459
2	2481	2219

Stop Event

1×	node limit

Counts

154 → 131

Calls

Call 1

Inputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 5))))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 5) (sin.f64 ky))))) (+.f64 (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 7) (sin.f64 ky)))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (sin.f64 kx) (sin.f64 th))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (.f64 (sin.f64 kx) (sin.f64 th)))) (/.f64 (sin.f64 kx) (sin.f64 th)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (.f64 (sin.f64 kx) (sin.f64 th)))) (/.f64 (sin.f64 kx) (sin.f64 th))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 ky 4) (.f64 (sin.f64 kx) (sin.f64 th)))) (.f64 1/8 (/.f64 (pow.f64 ky 4) (.f64 (pow.f64 (sin.f64 kx) 3) (sin.f64 th))))))
(-.f64 (+.f64 (.f64 1/45 (/.f64 (pow.f64 ky 6) (.f64 (sin.f64 kx) (sin.f64 th)))) (+.f64 (.f64 1/12 (/.f64 (pow.f64 ky 6) (.f64 (pow.f64 (sin.f64 kx) 3) (sin.f64 th)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 ky 6) (.f64 (pow.f64 (sin.f64 kx) 5) (sin.f64 th)))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 ky 2) (.f64 (sin.f64 kx) (sin.f64 th)))) (/.f64 (sin.f64 kx) (sin.f64 th)))))) (+.f64 (.f64 1/6 (/.f64 (pow.f64 ky 4) (.f64 (sin.f64 kx) (sin.f64 th)))) (.f64 1/8 (/.f64 (pow.f64 ky 4) (.f64 (pow.f64 (sin.f64 kx) 3) (sin.f64 th))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (sin.f64 ky) (sin.f64 th))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (.f64 (sin.f64 th) (sin.f64 ky)))) (/.f64 (sin.f64 ky) (sin.f64 th)))
(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (.f64 (sin.f64 th) (sin.f64 ky)))) (/.f64 (sin.f64 ky) (sin.f64 th))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)))) (.f64 1/6 (/.f64 (pow.f64 kx 4) (.f64 (sin.f64 th) (sin.f64 ky))))))
(-.f64 (+.f64 (.f64 1/45 (/.f64 (pow.f64 kx 6) (.f64 (sin.f64 th) (sin.f64 ky)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 kx 6) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 5)))) (+.f64 (.f64 1/12 (/.f64 (pow.f64 kx 6) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 kx 2) (.f64 (sin.f64 th) (sin.f64 ky)))) (/.f64 (sin.f64 ky) (sin.f64 th)))))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 kx 4) (.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 3)))) (.f64 1/6 (/.f64 (pow.f64 kx 4) (.f64 (sin.f64 th) (sin.f64 ky))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 th))
(+.f64 (.f64 1/6 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) th)) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 th)))
(+.f64 (.f64 1/6 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) th)) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 th)) (.f64 7/360 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (pow.f64 th 3)))))
(+.f64 (.f64 1/6 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) th)) (+.f64 (.f64 31/15120 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (pow.f64 th 5))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 th)) (.f64 7/360 (*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (pow.f64 th 3))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))

Outputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 3))))))
(-.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky) (.f64 (*.f64 (/.f64 (pow.f64 ky 3) (sin.f64 kx)) (sin.f64 th)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (-.f64 (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 5))) (fma.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)) (.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 5)))))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 3)))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (pow.f64 ky 5) (/.f64 (pow.f64 (sin.f64 kx) 5) (sin.f64 th))) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky (fma.f64 3/8 (/.f64 (pow.f64 ky 5) (/.f64 (pow.f64 (sin.f64 kx) 5) (sin.f64 th))) (.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (+.f64 (/.f64 1/4 (pow.f64 (sin.f64 kx) 2)) 1/120)))) (.f64 (.f64 (/.f64 (pow.f64 ky 3) (sin.f64 kx)) (sin.f64 th)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(-.f64 (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 5))) (fma.f64 3/8 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 5))) (+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (fma.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 3))) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 7))) (fma.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/5040 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 7))))))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (pow.f64 ky 5) (/.f64 (pow.f64 (sin.f64 kx) 5) (sin.f64 th))) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 7)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 7))) (fma.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/5040 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 7)))))))))
(-.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky (fma.f64 3/8 (/.f64 (pow.f64 ky 5) (/.f64 (pow.f64 (sin.f64 kx) 5) (sin.f64 th))) (.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (+.f64 (/.f64 1/4 (pow.f64 (sin.f64 kx) 2)) 1/120)))) (+.f64 (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 7)) (.f64 (.f64 (/.f64 (pow.f64 ky 3) (sin.f64 kx)) (sin.f64 th)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6))) (fma.f64 5/16 (.f64 (/.f64 (pow.f64 ky 7) (pow.f64 (sin.f64 kx) 5)) (sin.f64 th)) (.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 7)) (+.f64 (/.f64 13/240 (pow.f64 (sin.f64 kx) 2)) 1/5040)))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (sin.f64 th) (.f64 -1/2 (/.f64 (.f64 (sin.f64 th) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (sin.f64 th) (/.f64 (.f64 -1/2 (.f64 (sin.f64 th) (*.f64 kx kx))) (pow.f64 (sin.f64 ky) 2)))
(fma.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) -1/2 (sin.f64 th))
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(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2)) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (.f64 kx kx)) (pow.f64 (sin.f64 ky) 2)) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (pow.f64 kx 4) (/.f64 (pow.f64 (sin.f64 ky) 4) (sin.f64 th))) (sin.f64 th))) (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (pow.f64 kx 6))) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 1/45 (/.f64 (*.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (+.f64 (.f64 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (+.f64 1/6 (/.f64 3/8 (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)) (+.f64 (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))))) (.f64 (/.f64 (*.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)) (+.f64 1/45 (/.f64 1/4 (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 th (sin.f64 ky))) (.f64 -1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3)))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 th (sin.f64 ky)) (.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3))) -1/6))
(.f64 (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))) (-.f64 th (*.f64 (pow.f64 th 3) 1/6)))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 5))))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3)))))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 th)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))) (/.f64 1 (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))

prune148.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	167	8	175

Error

Counts

175 → 8

Alt Table

Status	Error	Program
	3.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	13.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (-.f64 (exp.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 1))
	14.5b	(/.f64 (sin.f64 ky) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (cbrt.f64 (pow.f64 (sin.f64 th) 2))) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))))
	3.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
	0.3b	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
▶	0.3b	(expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 4455 to 1926 computations (56.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
✓	0.1b	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series187.0ms (1.5%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
48.0ms	th	@	-inf	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
39.0ms	ky	@	inf	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
25.0ms	kx	@	-inf	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
22.0ms	ky	@	-inf	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
18.0ms	th	@	inf	(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

563×	`log-prod_binary64`
429×	`prod-diff_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
182×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	56
1	224	56
2	2804	56

Stop Event

1×	node limit

Counts

3 → 106

Calls

Call 1

Inputs

(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

(log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

(expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))

Outputs

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

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

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

simplify136.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

482×	`cancel-sign-sub-inv_binary64`
246×	`fma-neg_binary64`
218×	`unswap-sqr_binary64`
212×	`times-frac_binary64`
207×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	5124
1	847	5092
2	3566	5057

Stop Event

1×	node limit

Counts

214 → 121

Calls

Call 1

Inputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 5))))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3)))))
(-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/120 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 5) (sin.f64 ky))))) (+.f64 (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (pow.f64 th 7) (sin.f64 ky)))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))

Outputs
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(-.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 3)) (.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky) (fma.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3)) (.f64 1/6 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)))))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)))))
(+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (-.f64 (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 5))) (fma.f64 1/120 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 5))) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/6 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 3)) (.f64 1/6 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3)) (.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/120 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (sin.f64 kx)))))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 7))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5))) (+.f64 (.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3))) (.f64 1/5040 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 7)) (sin.f64 kx)))))))))
(-.f64 (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 3) (pow.f64 ky 5))) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 1/120 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 5))))))) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 7) (pow.f64 ky 7))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 kx) 5) (pow.f64 ky 7))) (fma.f64 13/240 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 3)) (.f64 1/5040 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) (pow.f64 ky 7))))))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 7)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 3)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)) (fma.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 13/240 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 7)) (.f64 1/5040 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 7)))))))))
(-.f64 (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 5)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 5)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 1/120 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 5)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)))) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 7)) (pow.f64 ky 7)) (fma.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3)) (fma.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 7)) (pow.f64 (sin.f64 kx) 5)) (fma.f64 13/240 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 7)) (.f64 1/5040 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 7)))))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (pow.f64 th 3) (sin.f64 ky)))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 -1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3)))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)) (.f64 (.f64 -1/6 (.f64 (sin.f64 ky) (pow.f64 th 3))) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(fma.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (.f64 -1/6 (.f64 (sin.f64 ky) (pow.f64 th 3))) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
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(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)) (.f64 (.f64 1/120 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 ky) (pow.f64 th 5)))) (.f64 -1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 3)))))
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(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)) (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (.f64 (sin.f64 ky) (pow.f64 th 5)) 1/120) (.f64 (.f64 -1/6 (.f64 (sin.f64 ky) (pow.f64 th 3))) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
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(-.f64 (fma.f64 1/120 (.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5))) (.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (fma.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3))) (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 7))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (sin.f64 th) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(-.f64 (sin.f64 th) (/.f64 (.f64 (.f64 1/2 (sin.f64 th)) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) 2)))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(+.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th))) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))))
(+.f64 (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))) (*.f64 1/45 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 6))))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 4)) (pow.f64 kx 6)) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 6)) (pow.f64 kx 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)
(-.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/2 (/.f64 (*.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 2))))
(+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (.f64 -1/2 (/.f64 (pow.f64 (sin.f64 th) 2) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 ky ky)))))
(+.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky) (/.f64 (.f64 -1/2 (pow.f64 (sin.f64 th) 2)) (/.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 ky ky))))
(fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky (/.f64 (.f64 -1/2 (pow.f64 (sin.f64 th) 2)) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 ky ky))))
(-.f64 (+.f64 (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx)) (.f64 1/3 (/.f64 (.f64 (pow.f64 (sin.f64 th) 3) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3))) (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx))) (.f64 1/2 (/.f64 (*.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 ky 2)) (pow.f64 (sin.f64 kx) 2))))))
(+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (-.f64 (/.f64 (.f64 1/3 (.f64 (pow.f64 ky 3) (pow.f64 (sin.f64 th) 3))) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (.f64 1/2 (/.f64 (pow.f64 (sin.f64 th) 2) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 ky ky))))))))
(-.f64 (fma.f64 1/3 (/.f64 (.f64 (pow.f64 ky 3) (pow.f64 (sin.f64 th) 3)) (pow.f64 (sin.f64 kx) 3)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) 3)) (pow.f64 ky 3)) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 ky ky)) (.f64 1/6 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3))))))
(-.f64 (fma.f64 1/3 (/.f64 (pow.f64 (sin.f64 th) 3) (pow.f64 (/.f64 (sin.f64 kx) ky) 3)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)) (fma.f64 1/2 (/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 kx) ky) 3)) (fma.f64 1/2 (.f64 (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (sin.f64 kx) 2)) (.f64 ky ky)) (.f64 1/6 (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (pow.f64 ky 3))))))
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(-.f64 (fma.f64 1/6 (/.f64 (pow.f64 (sin.f64 th) 2) (/.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 ky 4))) (+.f64 (/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky)) (fma.f64 1/2 (/.f64 (pow.f64 (sin.f64 th) 2) (/.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 ky 4))) (/.f64 (.f64 1/3 (.f64 (pow.f64 ky 3) (pow.f64 (sin.f64 th) 3))) (pow.f64 (sin.f64 kx) 3))))) (fma.f64 1/4 (/.f64 (pow.f64 (sin.f64 th) 4) (/.f64 (pow.f64 (sin.f64 kx) 4) (pow.f64 ky 4))) (fma.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (pow.f64 (sin.f64 kx) 3)) (fma.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (.f64 1/2 (/.f64 (pow.f64 (sin.f64 th) 2) (/.f64 (pow.f64 (sin.f64 kx) 2) (.f64 ky ky))))))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(-.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 1/2 (/.f64 (.f64 (pow.f64 th 2) (pow.f64 (sin.f64 ky) 2)) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
(+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky))) (.f64 -1/2 (/.f64 (.f64 th th) (/.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) (pow.f64 (sin.f64 ky) 2)))))
(fma.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)) (.f64 (/.f64 (.f64 th (.f64 th (pow.f64 (sin.f64 ky) 2))) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) -1/2))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
(log1p.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(log1p.f64 (.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
(log.f64 (+.f64 1 (sin.f64 th)))
(log1p.f64 (sin.f64 th))
(-.f64 (log.f64 (+.f64 1 (sin.f64 th))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (*.f64 (+.f64 1 (sin.f64 th)) (pow.f64 (sin.f64 ky) 2)))))
(+.f64 (log1p.f64 (sin.f64 th)) (.f64 -1/2 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) 2)))))
(+.f64 (log1p.f64 (sin.f64 th)) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (/.f64 (.f64 kx kx) (+.f64 (sin.f64 th) 1)))))
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(-.f64 (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 4))) (+.f64 (log1p.f64 (sin.f64 th)) (.f64 1/6 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 2)))))) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) 2))) (.f64 1/8 (*.f64 (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (+.f64 (sin.f64 th) 1) 2)) (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 4))))))
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(-.f64 (fma.f64 3/8 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 4))) (fma.f64 1/12 (.f64 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 4)) (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (+.f64 (sin.f64 th) 1) 2))) (fma.f64 3/16 (.f64 (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (sin.f64 ky) 6)) (/.f64 (pow.f64 kx 6) (pow.f64 (+.f64 (sin.f64 th) 1) 2))) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 2))) (log1p.f64 (sin.f64 th)))))) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 kx (/.f64 (pow.f64 (sin.f64 ky) 2) kx))) (fma.f64 1/45 (.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 2))) (fma.f64 1/4 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 4) (/.f64 (pow.f64 kx 6) (+.f64 (sin.f64 th) 1)))) (fma.f64 5/16 (.f64 (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 6)) (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1))) (fma.f64 1/8 (.f64 (/.f64 (pow.f64 kx 4) (pow.f64 (sin.f64 ky) 4)) (/.f64 (pow.f64 (sin.f64 th) 2) (pow.f64 (+.f64 (sin.f64 th) 1) 2))) (.f64 1/24 (.f64 (pow.f64 (/.f64 (sin.f64 th) (+.f64 (sin.f64 th) 1)) 3) (/.f64 (pow.f64 kx 6) (pow.f64 (sin.f64 ky) 6))))))))))
(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(log.f64 (+.f64 1 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))))
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(/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx))
(/.f64 (sin.f64 th) (/.f64 (sin.f64 kx) ky))
(*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky)
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(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 th (sin.f64 ky)))
(.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
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(fma.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (.f64 -1/6 (.f64 (sin.f64 ky) (pow.f64 th 3))) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
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(-.f64 (fma.f64 1/120 (.f64 (sin.f64 ky) (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (pow.f64 th 5))) (.f64 th (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))) (fma.f64 1/6 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 ky) (pow.f64 th 3))) (.f64 1/5040 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (*.f64 (sin.f64 ky) (pow.f64 th 7))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(sin.f64 th)
(-.f64 (sin.f64 th) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (sin.f64 th) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(-.f64 (sin.f64 th) (/.f64 (.f64 (.f64 1/2 (sin.f64 th)) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) 2)))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))))
(+.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (.f64 -1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(+.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th))) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))))
(+.f64 (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th)) (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (/.f64 (.f64 -1/2 (sin.f64 th)) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx)))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 2))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (+.f64 (.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4))) (+.f64 (.f64 5/16 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 6))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 2)) (pow.f64 (sin.f64 ky) 2))) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(-.f64 (fma.f64 1/6 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 4))) (+.f64 (sin.f64 th) (.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4))))) (fma.f64 1/4 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 4)) (fma.f64 5/16 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 6) (pow.f64 kx 6))) (fma.f64 1/2 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (.f64 kx kx))) (*.f64 1/45 (/.f64 (sin.f64 th) (/.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 kx 6))))))))
(-.f64 (fma.f64 1/6 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (pow.f64 kx 4)) (fma.f64 3/8 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 4)) (pow.f64 (sin.f64 ky) 4)) (sin.f64 th))) (fma.f64 1/4 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 4)) (pow.f64 kx 6)) (fma.f64 5/16 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 6)) (pow.f64 kx 6)) (fma.f64 1/2 (.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) 2)) (.f64 kx kx)) (.f64 1/45 (/.f64 (.f64 (sin.f64 th) (pow.f64 kx 6)) (pow.f64 (sin.f64 ky) 2)))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

prune170.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	181	8	189

Error

Counts

189 → 8

Alt Table

Status	Error	Program
	3.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	0.3b	(.f64 (sin.f64 th) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))
	13.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (-.f64 (exp.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 1))
	14.5b	(/.f64 (sin.f64 ky) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (cbrt.f64 (pow.f64 (sin.f64 th) 2))) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))))
	3.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	1.2b	(*.f64 (/.f64 (sin.f64 th) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 6228 to 3039 computations (51.2% saved)

regimes1.2s (9.6%)

Accuracy

Total 0.2b remaining (87.2%)

Threshold costs 0.2b (87.2%)

Counts

205 → 1

Compiler

Compiled 3216 to 954 computations (70.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	17	18

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1) (sin.f64 th))

Outputs
(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

end123.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 181 to 118 computations (34.8% saved)

Details

analyze1.7s (13.9%)

sample7.7s (62.8%)

preprocess38.0ms (0.3%)

simplify44.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series28.0ms (0.2%)

rewrite52.0ms (0.4%)

simplify57.0ms (0.5%)

prune163.0ms (1.3%)

localize9.0ms (0.1%)

series14.0ms (0.1%)

rewrite52.0ms (0.4%)

simplify57.0ms (0.5%)

prune169.0ms (1.4%)

localize9.0ms (0.1%)

series15.0ms (0.1%)

rewrite51.0ms (0.4%)

simplify60.0ms (0.5%)

prune148.0ms (1.2%)

localize10.0ms (0.1%)

series187.0ms (1.5%)

rewrite75.0ms (0.6%)

simplify136.0ms (1.1%)

prune170.0ms (1.4%)

regimes1.2s (9.6%)

simplify2.0ms (0%)

end123.0ms (1%)

Profiling