Metrics for Toniolo and Linder, Equation (3b), real

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze201.0ms (1.8%)

Memory

-1.6MiB live, 233.0MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	6
43.8%	43.7%	56.2%	0.1%	0%	0%	0%	7
53.1%	53%	46.8%	0.1%	0%	0%	0%	8
60.9%	60.8%	39%	0.1%	0%	0%	0%	9
60.9%	60.8%	39%	0.1%	0%	0%	0%	10
64.8%	64.7%	35.1%	0.1%	0%	0%	0%	11
68.4%	68.3%	31.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.9s (17.1%)

Memory

74.0MiB live, 2 069.9MiB allocated

Samples

1.4s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-sin: 678.0ms (60.5% of total)

ival-pow2: 191.0ms (17% of total)

ival-sqrt: 67.0ms (6% of total)

ival-div: 60.0ms (5.4% of total)

ival-add: 60.0ms (5.4% of total)

ival-mult: 56.0ms (5% of total)

ival-true: 6.0ms (0.5% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain330.0ms (2.9%)

Memory

-26.9MiB live, 273.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
12	-	1	(4.0302590981287154e-174 -1.1309364425919811e-160 -2.6827395873491353e+168)	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	0	-	`(sin.f64 kx)`
0	-	0	-	`(sin.f64 th)`
0	-	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	-	0	-	`th`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
0	-	0	-	`(sin.f64 ky)`
0	-	0	-	`ky`
0	-	0	-	`kx`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	uflow-rescue	11	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	65
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	67
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	11

Confusion

	Predicted +	Predicted -
+	11	1
-	0	244

Precision

1.0

Recall

0.9166666666666666

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	11	0	1
-	0	0	244

Precision?

1.0

Recall?

0.9166666666666666

Freqs

test

number	freq
0	245
1	11

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

159.0ms

512×

valid

Compiler

Compiled 218 to 56 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 127.0ms

ival-pow2: 55.0ms (43.3% of total)

ival-sin: 54.0ms (42.5% of total)

ival-sqrt: 8.0ms (6.3% of total)

ival-div: 3.0ms (2.4% of total)

ival-mult: 3.0ms (2.4% of total)

ival-add: 2.0ms (1.6% of total)

ival-true: 1.0ms (0.8% of total)

ival-assert: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess73.0ms (0.7%)

Memory

-1.8MiB live, 37.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	153
1	101	147
2	211	147
3	383	147
4	831	147
5	1949	147
6	2504	147
7	2781	147
8	2893	147
9	2943	147
10	2958	147
11	2958	147
0	13	16
0	22	16
1	28	16
2	32	16
3	33	16
0	33	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

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

Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 11 to 9 computations (18.2% saved)

prune1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.2%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	99.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

Status

Accuracy

Program

▶

95.2%

(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

▶

99.7%

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

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify3.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	7424	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
cost-diff	0	(sin.f64 th)
cost-diff	0	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	99
0	31	84
1	40	84
2	42	84
3	43	84
0	43	84

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(sin.f64 th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(sin.f64 th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th

localize75.0ms (0.7%)

Memory

-3.6MiB live, 77.0MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.17578125	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.1875	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	0.193691259768442	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	2.8372508843070467	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	0	(sin.f64 kx)
accuracy	0.03515625	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.14453125	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
accuracy	0.17578125	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

Samples

49.0ms

256×

valid

Compiler

Compiled 221 to 34 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-sin: 16.0ms (44.1% of total)

ival-pow2: 7.0ms (19.3% of total)

ival-hypot: 4.0ms (11% of total)

ival-div: 3.0ms (8.3% of total)

ival-mult: 3.0ms (8.3% of total)

ival-sqrt: 2.0ms (5.5% of total)

ival-add: 1.0ms (2.8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series38.0ms (0.3%)

Memory

8.4MiB live, 46.3MiB allocated

Counts

11 → 228

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf kx) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor 0 ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	th	@	0	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
5.0ms	ky	@	-inf	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
5.0ms	ky	@	0	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
4.0ms	kx	@	inf	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))
4.0ms	kx	@	0	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (pow (sin kx) 2) (pow (sin ky) 2))

simplify250.0ms (2.2%)

Memory

12.6MiB live, 201.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	347	4416
1	1109	4318
2	4087	4140
0	8078	3850

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)

Outputs
(sin.f64 th)
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (sin.f64 th) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)))
#s(literal 1 binary64)
(fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (.f64 kx (/.f64 kx (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(sin.f64 th)
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (sin.f64 th) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th)))
#s(literal 1 binary64)
(fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (.f64 kx (/.f64 kx (sin.f64 ky))) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
kx
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
(*.f64 kx kx)
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 kx kx))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
(sin.f64 kx)
(sin.f64 kx)
(sin.f64 kx)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
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th
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ky
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(sin.f64 kx)
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(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
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(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1/12 binary64) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(/.f64 ky (sin.f64 kx))
(fma.f64 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (-.f64 (/.f64 #s(literal -1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky ky) (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx)))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
(sin.f64 kx)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))
(fma.f64 (fma.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx))) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(*.f64 ky ky)
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 ky ky))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (*.f64 ky ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))

rewrite181.0ms (1.6%)

Memory

-12.2MiB live, 42.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	77
0	31	62
1	101	62
2	563	62
0	7571	62

Stop Event

1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Counts

11 → 365

Calls

Call 1

Inputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(sin.f64 th)
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))

Outputs
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eval144.0ms (1.3%)

Memory: -4.7MiB live, 106.5MiB allocated
Compiler: Compiled 17 233 to 1 710 computations (90.1% saved)

prune113.0ms (1%)

Memory

-11.9MiB live, 73.6MiB allocated

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	695	17	712
Fresh	0	0	0
Picked	1	1	2
Done	0	0	0
Total	696	18	714

Accuracy

99.9%

Counts

714 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	17.0%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	85.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	74.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) (sin.f64 ky))))
✓	99.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	57.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	63.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	26.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
	31.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
▶	94.6%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
▶	48.3%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	19.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1/12 binary64) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
▶	43.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
▶	92.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
▶	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 1 109 to 717 computations (35.3% saved)

simplify6.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(*.f64 (sin.f64 ky) th)
cost-diff	0	(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
cost-diff	0	(sin.f64 th)
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
cost-diff	0	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))
cost-diff	0	(sin.f64 th)
cost-diff	0	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	377
0	64	362
1	85	362
2	100	362
3	104	362
4	105	362
0	105	362

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
(sin.f64 th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
th
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) th)
(sin.f64 ky)
ky
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th

Outputs
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th))
(sin.f64 th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
th
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) th)
(sin.f64 ky)
ky
th
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))
#s(literal 1 binary64)
(fma.f64 (sin.f64 ky) (sin.f64 ky) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))
(sin.f64 kx)
kx
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 th)
th

localize142.0ms (1.3%)

Memory

2.5MiB live, 160.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.234375	(*.f64 (sin.f64 ky) (sin.f64 th))
accuracy	0.25390625	(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	2.758614997415752	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
accuracy	3.1838377045842825	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.25390625	(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	2.7602362376473097	(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
accuracy	3.1838377045842825	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	33.04450136040148	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
accuracy	0.03515625	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.14453125	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
accuracy	0.17578125	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	0	(sin.f64 th)
accuracy	43.88760230485984	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0.1875	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	0.25390625	(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	0.30306625976844204	(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
accuracy	3.1838377045842825	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Samples

116.0ms

256×

valid

Compiler

Compiled 741 to 69 computations (90.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 20.0ms (36.8% of total)

ival-sin: 16.0ms (29.4% of total)

ival-div: 4.0ms (7.4% of total)

ival-hypot: 4.0ms (7.4% of total)

ival-pow2: 4.0ms (7.4% of total)

ival-sqrt: 3.0ms (5.5% of total)

ival-add: 2.0ms (3.7% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series50.0ms (0.4%)

Memory

15.6MiB live, 54.0MiB allocated

Counts

19 → 492

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sin th) th) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) th) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 ky) (sin.f64 th)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
16.0ms	th	@	inf	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin ky) (sin th))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (pow (sin ky) 2) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin ky) (sin th)))
3.0ms	ky	@	0	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin ky) (sin th))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (pow (sin ky) 2) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin ky) (sin th)))
3.0ms	th	@	0	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin ky) (sin th))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (pow (sin ky) 2) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin ky) (sin th)))
3.0ms	th	@	-inf	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin ky) (sin th))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (pow (sin ky) 2) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin ky) (sin th)))
3.0ms	kx	@	inf	((* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (* (sin ky) (sin th))) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (pow (sin ky) 2) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin ky) (sin th)))

simplify258.0ms (2.3%)

Memory

4.5MiB live, 186.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	10997
1	1658	10636
2	6664	10325
0	8046	9946

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* th (sin ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky th) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(* ky th)
(* ky (+ th (* -1/6 (* (pow ky 2) th))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* 1/120 (* (pow ky 2) th))))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) th)) (* 1/120 th)))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 (pow (sin kx) 2))
(+ (* -1 (/ (pow ky 2) (pow (sin kx) 4))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6)))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6))))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* ky (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))

Outputs
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) kx (fma.f64 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (sin.f64 th)))
#s(literal 1 binary64)
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
#s(literal 1 binary64)
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
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(sin.f64 th)
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#s(literal 1 binary64)
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(sin.f64 th)
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th
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(sin.f64 th)
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(sin.f64 th)
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(/.f64 #s(literal 1 binary64) (sin.f64 ky))
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(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
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(sin.f64 ky)
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(*.f64 (sin.f64 ky) th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (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))

rewrite185.0ms (1.6%)

Memory

-32.8MiB live, 164.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	259
0	64	194
1	165	190
2	769	186
0	9288	186

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

19 → 556

Calls

Call 1

Inputs
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
(sin.f64 th)
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
#s(approx (sin th) th)
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(*.f64 (sin.f64 ky) th)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(*.f64 (sin.f64 ky) (sin.f64 th))

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eval911.0ms (8.1%)

Memory: -7.0MiB live, 502.1MiB allocated
Compiler: Compiled 72 544 to 4 151 computations (94.3% saved)

prune157.0ms (1.4%)

Memory

35.7MiB live, 269.1MiB allocated

Pruning

43 alts after pruning (37 fresh and 6 done)

	Pruned	Kept	Total
New	1 726	27	1 753
Fresh	2	10	12
Picked	0	5	5
Done	0	1	1
Total	1 728	43	1 771

Accuracy

99.9%

Counts

1 771 → 43

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	85.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	74.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) (sin.f64 ky))))
✓	99.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	57.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	63.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	26.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	31.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
✓	94.6%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
	17.0%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (sin.f64 ky))))
	44.2%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
	43.3%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
	31.4%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
	34.1%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
✓	48.3%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	27.7%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
▶	24.9%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
	17.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
▶	14.5%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	16.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
	46.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
	19.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1/12 binary64) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
✓	43.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	23.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
	12.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
	22.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	19.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
✓	92.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
	43.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx ( (sin ky) (sin th)) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 binary64))) (*.f64 (sin.f64 ky) th)))))
▶	16.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
	43.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	42.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	31.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	14.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
	16.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
▶	17.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))

Compiler

Compiled 2 908 to 1 863 computations (35.9% saved)

simplify120.0ms (1.1%)

Memory

-6.9MiB live, 191.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	128	(.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))
cost-diff	192	(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))
cost-diff	7296	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
cost-diff	0	(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff	0	#s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
cost-diff	0	(sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	538
0	97	518
1	145	470
2	215	470
3	321	460
4	545	460
5	1261	460
6	3005	460
7	5614	460
0	8126	423

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
#s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)
th
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
kx
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))
(sin.f64 ky)
ky
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx)
(/.f64 #s(literal 1/2 binary64) (sin.f64 ky))
#s(literal 1/2 binary64)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
#s(literal 1 binary64)
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(cos.f64 (*.f64 #s(literal 2 binary64) kx))
(*.f64 #s(literal 2 binary64) kx)
#s(literal 2 binary64)
kx
(.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))
#s(literal 4 binary64)
(*.f64 (sin.f64 ky) (sin.f64 th))
(sin.f64 ky)
ky
(sin.f64 th)
th

Outputs
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))
(sin.f64 ky)
ky
(sqrt.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1/2 binary64))
(cos.f64 (*.f64 kx #s(literal 2 binary64)))
(*.f64 kx #s(literal 2 binary64))
#s(literal 2 binary64)
kx
#s(literal -1/2 binary64)
#s(literal 1/2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
#s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)
th
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) #s(literal -1/2 binary64) #s(literal 1 binary64))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) #s(literal -1/2 binary64) #s(literal 1 binary64))
(*.f64 (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx)
kx
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))
(sin.f64 ky)
ky
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx)
(/.f64 #s(literal 1/2 binary64) (sin.f64 ky))
#s(literal 1/2 binary64)
kx
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (-.f64 (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal -1/4 binary64) (-.f64 (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 1 binary64)))
#s(literal 1 binary64)
(fma.f64 #s(literal -4 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 4 binary64))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))
(cos.f64 (*.f64 kx #s(literal 2 binary64)))
(*.f64 kx #s(literal 2 binary64))
#s(literal 2 binary64)
kx
(fma.f64 #s(literal -2 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))) #s(literal 2 binary64))
#s(literal 4 binary64)
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 ky)
ky
(sin.f64 th)
th

localize280.0ms (2.5%)

Memory

-1.1MiB live, 604.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	2.80368197591611	(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))
accuracy	15.701273633238722	(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))
accuracy	17.361838451267595	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
accuracy	50.56100696625365	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
accuracy	0.17578125	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))
accuracy	0.21484375	(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx)
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	45.20310133112928	#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
accuracy	2.413732526407154	(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	2.913427175255087	(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	46.063399015457456	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	33.04450136040148	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
accuracy	43.967789316288915	#s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)
accuracy	0.17578125	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.1875	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	2.8372508843070467	(sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	17.352075699973625	(fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))

Samples

94.0ms	67×	2	valid
78.0ms	121×	0	valid
61.0ms	68×	1	valid

Compiler

Compiled 974 to 115 computations (88.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 184.0ms

ival-mult: 42.0ms (22.8% of total)

ival-sin: 35.0ms (19% of total)

ival-cos: 30.0ms (16.3% of total)

ival-div: 19.0ms (10.3% of total)

adjust: 16.0ms (8.7% of total)

ival-add: 13.0ms (7.1% of total)

ival-sqrt: 11.0ms (6% of total)

ival-pow2: 8.0ms (4.3% of total)

ival-hypot: 7.0ms (3.8% of total)

ival-sub: 3.0ms (1.6% of total)

exact: 1.0ms (0.5% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series139.0ms (1.2%)

Memory

-19.7MiB live, 221.1MiB allocated

Counts

26 → 588

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sin th) th) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
31.0ms	ky	@	-inf	((* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (* 2 (- 1 (cos (* 2 kx)))) (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* kx (/ kx (pow (sin ky) 2))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ 1/2 (sin ky)) kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (- 1 (cos (* 2 kx))) (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))))
28.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (* 2 (- 1 (cos (* 2 kx)))) (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* kx (/ kx (pow (sin ky) 2))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ 1/2 (sin ky)) kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (- 1 (cos (* 2 kx))) (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))))
16.0ms	kx	@	-inf	((* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (* 2 (- 1 (cos (* 2 kx)))) (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* kx (/ kx (pow (sin ky) 2))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ 1/2 (sin ky)) kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (- 1 (cos (* 2 kx))) (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))))
9.0ms	kx	@	0	((* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (* 2 (- 1 (cos (* 2 kx)))) (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* kx (/ kx (pow (sin ky) 2))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ 1/2 (sin ky)) kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (- 1 (cos (* 2 kx))) (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))))
8.0ms	kx	@	inf	((* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx))))) (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) (* 2 (- 1 (cos (* 2 kx)))) (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* kx (/ kx (pow (sin ky) 2))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (/ 1/2 (sin ky)) kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (- 1 (cos (* 2 kx))) (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))))

simplify218.0ms (1.9%)

Memory

9.2MiB live, 401.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	871	12557
1	2806	12172
2	7115	12086
0	8321	11500

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 588

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(* 8 (pow kx 2))
(* (pow kx 2) (+ 8 (* -8/3 (pow kx 2))))
(* (pow kx 2) (+ 8 (* (pow kx 2) (- (* 16/45 (pow kx 2)) 8/3))))
(* (pow kx 2) (+ 8 (* (pow kx 2) (- (* (pow kx 2) (+ 16/45 (* -8/315 (pow kx 2)))) 8/3))))
(/ 1/2 (pow kx 2))
(/ (+ 1/2 (* 1/6 (pow kx 2))) (pow kx 2))
(/ (+ 1/2 (* (pow kx 2) (+ 1/6 (* 1/30 (pow kx 2))))) (pow kx 2))
(/ (+ 1/2 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 1/30 (* 1/189 (pow kx 2))))))) (pow kx 2))
(/ 1/8 (pow kx 2))
(/ (+ 1/8 (* 1/24 (pow kx 2))) (pow kx 2))
(/ (+ 1/8 (* (pow kx 2) (+ 1/24 (* 1/120 (pow kx 2))))) (pow kx 2))
(/ (+ 1/8 (* (pow kx 2) (+ 1/24 (* (pow kx 2) (+ 1/120 (* 1/756 (pow kx 2))))))) (pow kx 2))
(* 4 (pow kx 2))
(* (pow kx 2) (+ 4 (* -4/3 (pow kx 2))))
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 8/45 (pow kx 2)) 4/3))))
(* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 8/45 (* -4/315 (pow kx 2)))) 4/3))))
(pow kx 2)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(* 2 (pow kx 2))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))
(/ (sqrt 1/2) kx)
(/ (+ (sqrt 1/2) (* 1/12 (/ (pow kx 2) (sqrt 1/2)))) kx)
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx)
(/ (+ (sqrt 1/2) (* (pow kx 2) (+ (* (pow kx 2) (+ (* 1/2 (/ (* (pow kx 2) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))) (sqrt 1/2))) (* 1/2 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (sqrt 1/2))))) (* 1/12 (/ 1 (sqrt 1/2)))))) kx)
(/ (* (sin ky) (* (sin th) (sqrt 1/2))) kx)
(/ (+ (* 1/12 (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 1/2))) (* (sin ky) (* (sin th) (sqrt 1/2)))) kx)
(/ (+ (* (sin ky) (* (sin th) (sqrt 1/2))) (* (pow kx 2) (+ (* 1/12 (/ (* (sin ky) (sin th)) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2))))))) (sqrt 1/2)))))) kx)
(/ (+ (* (sin ky) (* (sin th) (sqrt 1/2))) (* (pow kx 2) (+ (* 1/12 (/ (* (sin ky) (sin th)) (sqrt 1/2))) (* (pow kx 2) (+ (* 1/2 (/ (* (sin ky) (* (sin th) (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))))) (sqrt 1/2))) (* 1/2 (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- 1/189 (* 1/12 (/ (- 1/30 (* 1/144 (/ 1 (pow (sqrt 1/2) 2)))) (pow (sqrt 1/2) 2))))))) (sqrt 1/2)))))))) kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(* 4 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(/ 1/4 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(* 2 (- 1 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(+ 1/2 (* -1/2 (cos (* 2 kx))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))) (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2)))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* ky (sin th)) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/6 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* (pow ky 2) (+ (* 1/120 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (+ (* 1/12 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (+ (* 1/2 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 4)))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (+ (* -1/12 (* (* (sin th) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (+ (* -1/240 (* (sin th) (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))) (* -1/5040 (* (sin th) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))))))))))
(* ky (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))
(* ky (+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* -1/6 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))
(* ky (+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))))))))))))))
(* ky (+ (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ (* -1/6 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (+ (* 1/12 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ (* 1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))))) (* (pow ky 2) (+ (* -1/2 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))) (+ (* 2/45 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (+ (* 2/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3))) (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 4))))))) (+ (* -1/12 (* (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (+ (* 1/3 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 2))) (* 3/4 (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))))) (+ (* -1/240 (sqrt (/ 1 (pow (+ 1/2 (* -1/2 (cos (* 2 kx)))) 3)))) (* -1/5040 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))))))))))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sqrt (+ 1/2 (* -1/2 (cos (* 2 kx)))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (* 1/2 (* (pow ky 2) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))))))
(+ (sqrt (+ 1/2 (* -1/2 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (* 1/2 (* (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx))))))) (+ 1/2 (* -1/2 (cos (* 2 kx)))))))) (sqrt (/ 1 (+ 1/2 (* -1/2 (cos (* 2 kx)))))))))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky th) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 kx) (+ (* 2/135 kx) (* 1/3 (+ (* -1/9 kx) (* 2/45 kx))))))) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (pow kx 2) (pow ky 2))
(/ (+ (* 1/3 (* (pow kx 2) (pow ky 2))) (pow kx 2)) (pow ky 2))
(/ (+ (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))) (* -1/3 (pow kx 2)))) (pow kx 2)) (pow ky 2))
(/ (+ (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))) (* -1/3 (pow kx 2)))) (pow kx 2)) (pow ky 2))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* 1/2 (/ kx ky))
(/ (+ (* 1/12 (* kx (pow ky 2))) (* 1/2 kx)) ky)
(/ (+ (* 1/2 kx) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (+ (* -1/36 kx) (* 1/120 kx)))) (* 1/12 kx)))) ky)
(/ (+ (* 1/2 kx) (* (pow ky 2) (+ (* 1/12 kx) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (+ (* -1/5040 kx) (+ (* 1/720 kx) (* 1/6 (+ (* -1/36 kx) (* 1/120 kx))))))) (* -1/2 (+ (* -1/36 kx) (* 1/120 kx)))))))) ky)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* ky (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* -1/6 (* (* (pow ky 2) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/120 (* (* (pow ky 2) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/6 (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/5040 (* (* (pow ky 2) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/120 (* (sin th) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(* (sin ky) (sqrt (/ 1 (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(sqrt (+ 1/2 (+ (* -1/2 (cos (* 2 kx))) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(/ (pow kx 2) (pow (sin ky) 2))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))

Outputs
(sin.f64 th)
(fma.f64 (/.f64 (.f64 (.f64 kx kx) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin.f64 ky)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
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(sin.f64 th)
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th
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(sin.f64 th)
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#s(literal 1 binary64)
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#s(literal 1 binary64)
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(sin.f64 th)
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#s(literal 1 binary64)
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
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(*.f64 kx kx)
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(sin.f64 ky)
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(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(sin.f64 th)
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 th) (sin.f64 ky)))

rewrite89.0ms (0.8%)

Memory

-0.1MiB live, 156.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	452
0	97	430
1	334	336
0	2065	276

Stop Event

1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Counts

26 → 306

Calls

Call 1

Inputs
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(sin.f64 ky)
(sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
#s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th)
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sin th) th)
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))
(/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))
(fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))
(.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th)))

Outputs
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eval203.0ms (1.8%)

Memory: 4.6MiB live, 475.1MiB allocated
Compiler: Compiled 44 636 to 3 037 computations (93.2% saved)

prune124.0ms (1.1%)

Memory

-7.2MiB live, 361.4MiB allocated

Pruning

68 alts after pruning (64 fresh and 4 done)

	Pruned	Kept	Total
New	1 019	41	1 060
Fresh	9	23	32
Picked	4	1	5
Done	3	3	6
Total	1 035	68	1 103

Accuracy

100.0%

Counts

1 103 → 68

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
	95.6%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	94.8%	(.f64 (/.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) (sin.f64 th))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	41.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
	43.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
	41.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
	43.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	72.6%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))) (sin.f64 th))
	32.9%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
	74.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) (sin.f64 ky))))
✓	99.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
▶	57.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	63.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	26.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	31.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
	44.2%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
	43.3%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
	31.4%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
	34.1%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	29.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
✓	48.3%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
▶	27.7%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	18.3%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
	18.3%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
	18.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
	25.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
	25.2%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
	17.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
	18.1%	(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
	14.4%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	9.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	15.5%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
▶	15.1%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	9.9%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	9.8%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	10.9%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	15.7%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	16.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
	3.1%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
▶	2.8%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
	22.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	19.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
	20.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	17.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	43.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	13.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
	16.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
	14.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
	31.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	16.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
✓	17.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
	15.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
	13.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
	12.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
	37.6%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
	72.4%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	29.4%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))

Compiler

Compiled 4 692 to 3 152 computations (32.8% saved)

simplify8.0ms (0.1%)

Memory

19.8MiB live, 19.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
cost-diff	0	(sin.f64 th)
cost-diff	0	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
cost-diff	0	#s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
cost-diff	0	(fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	#s(approx (sin th) th)
cost-diff	0	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
cost-diff	0	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
cost-diff	0	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
cost-diff	0	(sin.f64 th)
cost-diff	0	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	359
0	75	359
1	107	359
2	145	359
3	196	359
4	218	359
0	218	356

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(sin.f64 th)
th
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sin.f64 kx)
kx
(sin.f64 ky)
ky
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky))))
kx
(/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(*.f64 ky ky)
ky
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
#s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 kx kx)
kx
(/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
#s(literal -1/2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))
(sin.f64 kx)
kx
#s(approx (sin ky) ky)
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(sin.f64 th)
th
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))
(sin.f64 kx)
kx
#s(approx (sin ky) ky)

Outputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(sin.f64 th)
th
(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
kx
(sin.f64 ky)
ky
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))) kx #s(literal 1 binary64))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))) kx #s(literal 1 binary64)))
(fma.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))) kx #s(literal 1 binary64))
(/.f64 (.f64 kx kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))
kx
(/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(*.f64 ky ky)
ky
#s(literal -1/2 binary64)
#s(literal 1 binary64)
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
#s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(*.f64 kx kx)
kx
(/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
#s(literal -1/2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 ky)
ky
#s(literal 2 binary64)
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) #s(approx (sin th) th))
#s(approx (sin th) th)
th
(/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))
(sin.f64 kx)
kx
#s(approx (sin ky) ky)
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) (sin.f64 th))
(sin.f64 th)
th
(/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx)))
(sin.f64 ky)
ky
(hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))
(sin.f64 kx)
kx
#s(approx (sin ky) ky)

localize125.0ms (1.1%)

Memory

13.3MiB live, 166.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.03515625	(hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))
accuracy	0.14453125	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
accuracy	0.17578125	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
accuracy	27.609222211694103	#s(approx (sin ky) ky)
accuracy	0.14453125	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
accuracy	0.17578125	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
accuracy	27.609222211694103	#s(approx (sin ky) ky)
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	7.947888133793999	(.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	25.62452550634642	#s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	46.063399015457456	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
accuracy	2.913427175255087	(/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
accuracy	27.352420846551396	#s(approx (pow (sin ky) 2) (*.f64 ky ky))
accuracy	33.11230011016728	#s(approx (sin th) th)
accuracy	46.063399015457456	#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0	(sin.f64 kx)
accuracy	0.03515625	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.11328125	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
accuracy	0.15853500976844204	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))

Samples

96.0ms

256×

valid

Compiler

Compiled 705 to 73 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 39.0ms (52.5% of total)

ival-sin: 20.0ms (26.9% of total)

ival-div: 7.0ms (9.4% of total)

ival-hypot: 4.0ms (5.4% of total)

ival-pow2: 2.0ms (2.7% of total)

ival-add: 1.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series47.0ms (0.4%)

Memory

-9.5MiB live, 109.4MiB allocated

Counts

21 → 492

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sin th) th) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (sin.f64 kx) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (pow (sin ky) 2) (*.f64 ky ky)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (sin ky) ky) #<representation binary64>) () ())
#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 kx) (#s(alt #<batchref> (patch (.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())) ())
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#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (pow (sin ky) 2) (*.f64 ky ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (pow (sin ky) 2) (*.f64 ky ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (pow (sin ky) 2) (*.f64 ky ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (pow (sin ky) 2) (*.f64 ky ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sin ky) ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sin ky) ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sin ky) ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch #s(approx (sin ky) ky) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf ky) (#s(alt #<batchref> (patch (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
10.0ms	kx	@	inf	((/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin kx) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
6.0ms	ky	@	inf	((/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin kx) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
4.0ms	kx	@	-inf	((/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin kx) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
4.0ms	ky	@	-inf	((/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin kx) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
3.0ms	kx	@	0	((/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin ky) (* (sin th) (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (sin kx) (pow (sin ky) 2) (/ kx (pow (sin ky) 2)) (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

simplify193.0ms (1.7%)

Memory

-22.8MiB live, 304.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	459	9982
1	1453	9670
2	5500	9280
0	8227	8740

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 492

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 kx) (+ (* 2/135 kx) (* 1/3 (+ (* -1/9 kx) (* 2/45 kx))))))) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* -1/6 (* (pow kx 2) (pow ky 2)))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))

Outputs
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) kx (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
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(/.f64 ky (sin.f64 kx))
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ky
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) ky)
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
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(*.f64 ky ky)
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(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky))
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(/.f64 kx (*.f64 ky ky))
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(/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))
(.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky))
(/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))
(/.f64 (fma.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)) (.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 kx kx) #s(literal -2/189 binary64))) (.f64 ky ky) (.f64 (.f64 kx kx) #s(literal -1/30 binary64))))) (.f64 ky ky))
ky
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) ky)
(sin.f64 kx)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))
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(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
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(sin.f64 ky)
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(sin.f64 ky)
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64))
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(sin.f64 ky)
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite152.0ms (1.4%)

Memory

18.6MiB live, 257.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	271
0	75	271
1	225	271
2	1351	257
0	9012	254

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

21 → 391

Calls

Call 1

Inputs
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(sin.f64 th)
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (sin th) th)
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
(fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
#s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
(sin.f64 ky)
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(sin.f64 kx)
#s(approx (pow (sin ky) 2) (*.f64 ky ky))
(/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky)))
(.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
#s(approx (sin ky) ky)
(hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))

Outputs
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eval216.0ms (1.9%)

Memory: 24.8MiB live, 334.2MiB allocated
Compiler: Compiled 39 313 to 2 261 computations (94.2% saved)

prune125.0ms (1.1%)

Memory

-1.0MiB live, 278.2MiB allocated

Pruning

83 alts after pruning (77 fresh and 6 done)

	Pruned	Kept	Total
New	1 172	26	1 198
Fresh	8	51	59
Picked	3	2	5
Done	0	4	4
Total	1 183	83	1 266

Accuracy

100.0%

Counts

1 266 → 83

Alt Table

Click to see full alt table

Status	Accuracy	Program
	56.9%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
	34.1%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
	31.9%	(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
	48.3%	(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
	5.7%	(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
	95.6%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	94.8%	(.f64 (/.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) (sin.f64 th))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	41.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
	43.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
	41.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
	43.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	85.6%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	72.6%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))) (sin.f64 th))
	32.9%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
	5.6%	(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
	13.2%	(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
	74.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) (sin.f64 ky))))
✓	99.7%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	63.9%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	39.0%	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
	69.8%	(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	26.0%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
	31.8%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
	44.2%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
	43.3%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
	31.4%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
	34.1%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	29.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
	3.0%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
	27.8%	(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓	48.3%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	27.7%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	22.2%	(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
	18.3%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
	18.3%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
	18.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
	25.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
	17.6%	(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
	26.3%	(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	34.5%	(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	18.1%	(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
	5.7%	(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
	15.5%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
✓	15.1%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	9.9%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	9.9%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	15.7%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
	16.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
	11.1%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
	2.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
	3.1%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
	3.2%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
	2.4%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
	2.3%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
	2.8%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
	1.8%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
	2.0%	(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
	45.8%	#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
	22.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	19.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
	17.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	43.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	13.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
	16.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
	14.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
	31.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	16.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
✓	17.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
	15.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
	13.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
	12.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
	37.6%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
	72.4%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	29.4%	#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))

Compiler

Compiled 6 854 to 2 537 computations (63% saved)

regimes340.0ms (3%)

Memory

-5.1MiB live, 620.4MiB allocated

Counts

113 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx ( (sin ky) (sin th)) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 binary64))) (*.f64 (sin.f64 ky) th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 2 binary64))) (.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) #s(literal -1/12 binary64) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) #s(literal -1/2 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))

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

Calls

9 calls:

53.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
41.0ms	ky
34.0ms	th
34.0ms	(sin.f64 kx)
34.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
99.7%	1	`kx`
99.7%	1	`ky`
99.7%	1	`th`
99.7%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
99.7%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
99.7%	1	`(sin.f64 ky)`
99.7%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
99.7%	1	`(sin.f64 kx)`
99.7%	1	`(sin.f64 th)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes294.0ms (2.6%)

Memory

-10.5MiB live, 477.7MiB allocated

Counts

93 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
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(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

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

Calls

9 calls:

53.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
46.0ms	(sin.f64 ky)
31.0ms	th
29.0ms	(sin.f64 th)
26.0ms	kx

Results

Accuracy	Segments	Branch
99.6%	1	`kx`
99.6%	1	`ky`
99.6%	1	`th`
99.6%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
99.6%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
99.6%	1	`(sin.f64 ky)`
99.6%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
99.6%	1	`(sin.f64 kx)`
99.6%	1	`(sin.f64 th)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes238.0ms (2.1%)

Memory

23.7MiB live, 459.2MiB allocated

Counts

92 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64))) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th))

Outputs

(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))

Calls

9 calls:

27.0ms	(sin.f64 ky)
27.0ms	kx
27.0ms	ky
26.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
26.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
87.6%	3	`th`
99.1%	2	`kx`
99.1%	2	`ky`
88.3%	5	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
99.6%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
99.1%	3	`(sin.f64 ky)`
99.1%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
99.1%	3	`(sin.f64 kx)`
87.8%	4	`(sin.f64 th)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes192.0ms (1.7%)

Memory

-22.9MiB live, 291.2MiB allocated

Counts

88 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(literal 1/2 binary64)))))))

Outputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

Calls

6 calls:

44.0ms	(sin.f64 kx)
39.0ms	ky
26.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
26.0ms	(sin.f64 ky)
24.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
91.1%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
85.3%	2	`(sin.f64 ky)`
85.2%	3	`(sin.f64 kx)`
85.4%	2	`ky`
85.2%	2	`kx`
85.2%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`

Compiler

Compiled 23 to 31 computations (-34.8% saved)

regimes28.0ms (0.3%)

Memory

35.7MiB live, 73.2MiB allocated

Counts

85 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
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(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(approx (sin ky) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 ky) (sin.f64 th))))

Outputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

Calls

1 calls:

23.0ms

(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
91.0%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes305.0ms (2.7%)

Memory

-155.1MiB live, 63.6MiB allocated

Counts

81 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))

Outputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

Calls

1 calls:

22.0ms

(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
91.0%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes26.0ms (0.2%)

Memory

22.2MiB live, 60.2MiB allocated

Counts

80 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

Outputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))

Calls

1 calls:

21.0ms

(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
90.9%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes237.0ms (2.1%)

Memory

-12.3MiB live, 382.1MiB allocated

Counts

79 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

Outputs
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))

Calls

8 calls:

52.0ms	th
35.0ms	ky
27.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
26.0ms	(sin.f64 th)
24.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
73.5%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
83.6%	3	`(sin.f64 th)`
69.8%	1	`kx`
69.8%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
79.8%	2	`(sin.f64 ky)`
78.3%	2	`ky`
83.6%	2	`th`
83.2%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 40 to 47 computations (-17.5% saved)

regimes159.0ms (1.4%)

Memory

-1.3MiB live, 304.1MiB allocated

Counts

78 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) (fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2))) (sqrt.f64 (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 4 binary64)) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) #s(approx ( 2 (- 1 (cos (* 2 kx)))) (.f64 #s(literal 4 binary64) (.f64 kx kx))))) #s(literal 4 binary64))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 4 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/315 binary64) #s(literal 2/45 binary64)) (.f64 ky ky) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky)))))) (sin.f64 th))

Outputs

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (*.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))

(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))

Calls

6 calls:

31.0ms	(sin.f64 th)
25.0ms	(sin.f64 ky)
23.0ms	(sin.f64 kx)
23.0ms	th
22.0ms	ky

Results

Accuracy	Segments	Branch
71.7%	2	`ky`
76.9%	2	`(sin.f64 ky)`
76.9%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
69.8%	1	`(sin.f64 th)`
69.8%	1	`(sin.f64 kx)`
69.8%	1	`th`

Compiler

Compiled 21 to 29 computations (-38.1% saved)

regimes95.0ms (0.8%)

Memory

-8.5MiB live, 202.6MiB allocated

Counts

65 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))) (sin.f64 ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 #s(approx (sqrt (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)) (sin.f64 ky)))
(/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)) (sin.f64 ky)))
(.f64 #s(approx (sin th) th) (.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky)))))
(.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(approx (sin th) th)) (/.f64 #s(literal -1 binary64) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 ky))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))

Outputs
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))

Calls

4 calls:

23.0ms	(sin.f64 ky)
19.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
17.0ms	ky
17.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Results

Accuracy	Segments	Branch
69.8%	1	`ky`
69.8%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
69.8%	1	`(sin.f64 ky)`
69.8%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 32 to 31 computations (3.1% saved)

regimes142.0ms (1.3%)

Memory

35.8MiB live, 272.1MiB allocated

Counts

51 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))

Outputs

(*.f64 #s(approx (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))

Calls

9 calls:

18.0ms	th
17.0ms	kx
17.0ms	ky
16.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
52.1%	2	`(sin.f64 ky)`
50.8%	3	`(sin.f64 th)`
59.6%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
59.8%	3	`kx`
61.4%	3	`(sin.f64 kx)`
55.5%	4	`th`
59.8%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
51.1%	2	`ky`
54.6%	5	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes62.0ms (0.5%)

Memory

-13.9MiB live, 106.1MiB allocated

Counts

49 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) kx) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky))))))

Outputs

(*.f64 #s(approx (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))

Calls

4 calls:

15.0ms	(sin.f64 kx)
15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
15.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
13.0ms	kx

Results

Accuracy	Segments	Branch
59.6%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
59.5%	3	`kx`
59.5%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
59.6%	3	`(sin.f64 kx)`

Compiler

Compiled 20 to 24 computations (-20% saved)

regimes17.0ms (0.2%)

Memory

-5.6MiB live, 32.4MiB allocated

Counts

44 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))

Outputs

#s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (*.f64 (sin.f64 th) ky)))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))

Calls

1 calls:

14.0ms

(sin.f64 kx)

Results

Accuracy	Segments	Branch
59.6%	3	`(sin.f64 kx)`

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes55.0ms (0.5%)

Memory

9.6MiB live, 90.8MiB allocated

Counts

43 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sin.f64 th)) (/.f64 (sin.f64 ky) kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (sqrt ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (/.f64 (sqrt.f64 #s(literal 1/2 binary64)) kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx ( (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4) (/.f64 #s(literal 1/2 binary64) (.f64 kx kx)))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) #s(approx (sin ky) ky)) kx) kx (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx #s(approx (sin ky) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (*.f64 (sin.f64 ky) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (sqrt (* (/ 1 (+ (* (- 1 (cos (* 2 kx))) 2) (* 2 (- 1 (cos (* 2 kx)))))) 4)) (* (sin ky) (sin th))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))

Outputs

(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

4 calls:

15.0ms	(sin.f64 kx)
13.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
12.0ms	kx
12.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
48.9%	2	`kx`
48.9%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
56.1%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
53.7%	3	`(sin.f64 kx)`

Compiler

Compiled 20 to 24 computations (-20% saved)

regimes13.0ms (0.1%)

Memory

-19.9MiB live, 18.5MiB allocated

Counts

31 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(*.f64 #s(approx (sin th) th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal -2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (*.f64 (pow.f64 (/.f64 kx (sin.f64 ky)) #s(literal 2 binary64)) #s(literal -1/2 binary64)))) #s(approx (sin th) th))

Outputs

(*.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

1 calls:

9.0ms

(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
56.0%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes74.0ms (0.7%)

Memory

28.9MiB live, 115.1MiB allocated

Counts

24 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))

Outputs

(*.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

9 calls:

13.0ms	(sin.f64 th)
9.0ms	(sin.f64 kx)
7.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
7.0ms	(sin.f64 ky)
7.0ms	th

Results

Accuracy	Segments	Branch
39.0%	2	`kx`
39.0%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
34.8%	3	`(sin.f64 th)`
39.3%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
39.8%	2	`ky`
39.1%	3	`(sin.f64 kx)`
40.2%	2	`(sin.f64 ky)`
34.8%	3	`th`
42.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes12.0ms (0.1%)

Memory

-22.9MiB live, 15.2MiB allocated

Counts

23 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64)))))))
(.f64 #s(approx (sin th) (sin.f64 th)) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))) #s(literal -1 binary64)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx kx) #s(literal 1/2 binary64))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 kx (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (/.f64 (*.f64 kx #s(literal -1/2 binary64)) #s(literal 1/2 binary64))))))

Outputs

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

1 calls:

10.0ms

(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))

Results

Accuracy	Segments	Branch
42.3%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes50.0ms (0.4%)

Memory

5.4MiB live, 81.9MiB allocated

Counts

15 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))

Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

9 calls:

7.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
7.0ms	(sin.f64 th)
5.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
5.0ms	kx
5.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
31.4%	1	`th`
31.4%	1	`(sin.f64 th)`
31.4%	1	`(sin.f64 kx)`
31.4%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
31.4%	1	`kx`
31.4%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
31.4%	1	`ky`
31.4%	1	`(sin.f64 ky)`
31.4%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes44.0ms (0.4%)

Memory

20.4MiB live, 103.0MiB allocated

Accuracy

Total -10.1b remaining (-19.1%)

Threshold costs -10.1b (-19.1%)

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (.f64 (/.f64 (.f64 kx kx) ky) (/.f64 #s(literal -1/2 binary64) ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (*.f64 (/.f64 kx ky) (/.f64 kx ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64))) (.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal 1/3 binary64) (.f64 kx kx)) (.f64 ky ky) (.f64 kx kx)) (*.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx (/.f64 kx #s(approx (pow (sin ky) 2) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (*.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 (.f64 kx #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (.f64 kx #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (+ (* (* kx (/ kx (pow (sin ky) 2))) -1/2) 1) #s(approx (* (* kx kx) (/ -1/2 (pow (sin ky) 2))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) ky) ky)) (.f64 ky ky))) (*.f64 ky ky))))))
(.f64 #s(approx (sin th) th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (fma.f64 #s(approx (* kx (/ kx (pow (sin ky) 2))) (/.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) (.f64 kx kx))) (.f64 ky ky) (.f64 kx kx)) (.f64 ky ky))) #s(literal -1/2 binary64) #s(literal 1 binary64))))

Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))

Calls

9 calls:

6.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
6.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
4.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
4.0ms	(sin.f64 ky)
4.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
17.1%	1	`(sin.f64 ky)`
17.1%	1	`(sin.f64 kx)`
17.1%	1	`th`
17.1%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
17.1%	1	`(sin.f64 th)`
17.1%	1	`ky`
17.1%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
17.1%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
17.1%	1	`kx`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch29.0ms (0.3%)

Memory

-36.9MiB live, 2.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.156655347281281e-12	1.425024091928207e-11

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch2.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	8.03361415876508e-7	0.02663687404445355
0.0ms	-0.40681052215028457	-0.37542087347353453
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	8.03361415876508e-7	0.02663687404445355
0.0ms	-0.40681052215028457	-0.37542087347353453
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	8.03361415876508e-7	0.02663687404445355
0.0ms	-0.40681052215028457	-0.37542087347353453
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	8.03361415876508e-7	0.02663687404445355
0.0ms	-0.40681052215028457	-0.37542087347353453
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch67.0ms (0.6%)

Memory

4.1MiB live, 43.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
65.0ms	8.291749886389874e-5	0.0015189046549898954

Samples

14.0ms

112×

valid

Compiler

Compiled 215 to 172 computations (20% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-sin: 6.0ms (54.3% of total)

ival-pow2: 2.0ms (18.1% of total)

ival-div: 1.0ms (9% of total)

ival-add: 1.0ms (9% of total)

ival-mult: 1.0ms (9% of total)

ival-sqrt: 1.0ms (9% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.40681052215028457	-0.37542087347353453

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.9159391300967946e-96	4.328346283133866e-95
0.0ms	-0.019202326582660433	-0.007003597427198084

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.9159391300967946e-96	4.328346283133866e-95
0.0ms	-0.019202326582660433	-0.007003597427198084

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.9159391300967946e-96	4.328346283133866e-95
0.0ms	-0.019202326582660433	-0.007003597427198084

Compiler

Compiled 19 to 18 computations (5.3% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.03361415876508e-7	0.02663687404445355

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.03361415876508e-7	0.02663687404445355

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.1365965008395634e-15	5.2989672465027515e-15

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.1365965008395634e-15	5.2989672465027515e-15

Compiler

Compiled 19 to 19 computations (0% saved)

simplify32.0ms (0.3%)

Memory

4.1MiB live, 45.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	1293
1	188	1293
2	198	1293
3	204	1293
4	208	1293
5	209	1293

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 4951760157141521/1237940039285380274899124224 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))))))
(if (<=.f64 th #s(literal 3504881374004815/36893488147419103232 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))))
(*.f64 (sin.f64 th) (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th)) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th)) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) ky))) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (.f64 (/.f64 th (sin.f64 kx)) ky))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 4951760157141521/1237940039285380274899124224 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) (fma.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(approx (sin th) th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))) (sin.f64 th))))))
(if (<=.f64 th #s(literal 3504881374004815/36893488147419103232 binary64)) (.f64 #s(approx (sin th) th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/9007199254740992 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) th))) (.f64 (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th)))
(*.f64 (/.f64 #s(approx (sin ky) ky) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))) (sin.f64 th))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th)) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (+ ( (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))) ky)) (sin.f64 th)) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))))
(if (<=.f64 (sin.f64 kx) #s(literal -5764607523034235/576460752303423488 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (+ (* (cos (* 2 kx)) -1/2) 1/2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal -1/2 binary64) #s(literal 1/2 binary64)))))) (if (<=.f64 (sin.f64 kx) #s(literal 6012269011901013/1202453802380202612679414065556140558016349465041059773802132977424491020858679523053413887173001575952350707712 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 kx))) #s(approx (sin th) th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (.f64 (/.f64 th (sin.f64 kx)) ky))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) th))

soundness1.5s (12.9%)

Memory

-12.0MiB live, 813.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	10997
1	1658	10636
2	6664	10325
0	8046	9946
0	347	4416
1	1109	4318
2	4087	4140
0	8078	3850
0	60	452
0	97	430
1	334	336
0	2065	276
0	16	77
0	31	62
1	101	62
2	563	62
0	7571	62
0	459	9982
1	1453	9670
2	5500	9280
0	8227	8740
0	13	16
0	22	16
1	28	16
2	32	16
3	33	16
0	33	11
0	871	12557
1	2806	12172
2	7115	12086
0	8321	11500

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 3 091 to 1 236 computations (60% saved)

preprocess216.0ms (1.9%)

Memory

21.4MiB live, 334.2MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 2 882 to 562 computations (80.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze201.0ms (1.8%)

sample1.9s (17.1%)

explain330.0ms (2.9%)

preprocess73.0ms (0.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize75.0ms (0.7%)

series38.0ms (0.3%)

simplify250.0ms (2.2%)

rewrite181.0ms (1.6%)

eval144.0ms (1.3%)

prune113.0ms (1%)

simplify6.0ms (0.1%)

localize142.0ms (1.3%)

series50.0ms (0.4%)

simplify258.0ms (2.3%)

rewrite185.0ms (1.6%)

eval911.0ms (8.1%)

prune157.0ms (1.4%)

simplify120.0ms (1.1%)

localize280.0ms (2.5%)

series139.0ms (1.2%)

simplify218.0ms (1.9%)

rewrite89.0ms (0.8%)

eval203.0ms (1.8%)

prune124.0ms (1.1%)

simplify8.0ms (0.1%)

localize125.0ms (1.1%)

series47.0ms (0.4%)

simplify193.0ms (1.7%)

rewrite152.0ms (1.4%)

eval216.0ms (1.9%)

prune125.0ms (1.1%)

regimes340.0ms (3%)

regimes294.0ms (2.6%)

regimes238.0ms (2.1%)

regimes192.0ms (1.7%)

regimes28.0ms (0.3%)

regimes305.0ms (2.7%)

regimes26.0ms (0.2%)

regimes237.0ms (2.1%)

regimes159.0ms (1.4%)

regimes95.0ms (0.8%)

regimes142.0ms (1.3%)

regimes62.0ms (0.5%)

regimes17.0ms (0.2%)

regimes55.0ms (0.5%)

regimes13.0ms (0.1%)

regimes74.0ms (0.7%)

regimes12.0ms (0.1%)

regimes50.0ms (0.4%)

regimes44.0ms (0.4%)

bsearch29.0ms (0.3%)

bsearch2.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch67.0ms (0.6%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify32.0ms (0.3%)

soundness1.5s (12.9%)

preprocess216.0ms (1.9%)

end0.0ms (0%)

Profiling