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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze236.0ms (2.1%)

Memory

-12.4MiB live, 338.9MiB 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)

sample1.5s (13.8%)

Memory

93.2MiB live, 2 115.6MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 999.0ms

ival-sin: 576.0ms (57.7% of total)

ival-pow2: 168.0ms (16.8% of total)

ival-mult: 80.0ms (8% of total)

ival-div: 71.0ms (7.1% of total)

ival-sqrt: 61.0ms (6.1% of total)

ival-add: 34.0ms (3.4% of total)

ival-true: 6.0ms (0.6% of total)

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

Bogosity

explain184.0ms (1.6%)

Memory

-35.7MiB live, 293.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
14	-	-	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	-	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	-	`(sin.f64 kx)`
0	-	-	`(sin.f64 th)`
0	-	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
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	-	-	`th`
0	-	-	`#s(literal 2 binary64)`
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	-	-	`(sin.f64 ky)`
0	-	-	`ky`
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	14	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	50
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	65
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	14

Confusion

	Predicted +	Predicted -
+	14	0
-	0	242

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	14	0	0
-	0	0	242

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	242
1	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

85.0ms

512×

valid

Compiler

Compiled 155 to 43 computations (72.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-sin: 36.0ms (54.7% of total)

ival-div: 12.0ms (18.2% of total)

ival-pow2: 9.0ms (13.7% of total)

ival-mult: 3.0ms (4.6% of total)

ival-sqrt: 3.0ms (4.6% of total)

ival-add: 2.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess73.0ms (0.6%)

Memory

5.9MiB live, 44.2MiB allocated

Algorithm

1×	egg-herbie

Rules

390×	`unsub-neg`
362×	`times-frac`
340×	`associate-l`
334×	`associate-r`
280×	`distribute-lft-in`

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

Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 19 to 13 computations (31.6% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.4%	(*.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 19 to 13 computations (31.6% saved)

simplify4.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 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	7296	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Rules

16×	`lower-*.f32`
14×	`lower-*.f64`
6×	`lift-sin.f64`
6×	`*-commutative`
6×	`lower-sin.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
0	22	66
1	28	66
2	32	66
3	33	66
0	33	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

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

localize51.0ms (0.5%)

Memory

-1.5MiB live, 79.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1875	(/.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	0.21875	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	0.25390625	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	3.3997881767730727	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

43.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sin: 16.0ms (48.2% of total)

ival-pow2: 7.0ms (21.1% of total)

ival-mult: 5.0ms (15.1% of total)

ival-sqrt: 2.0ms (6% of total)

ival-div: 1.0ms (3% of total)

ival-add: 1.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

series33.0ms (0.3%)

Memory

8.3MiB live, 46.6MiB allocated

Counts

6 → 120

Calls

Call 1

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

Outputs
#s(alt (sin ky) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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 (+ (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)))))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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 (+ (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)))))) (taylor 0 kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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 (sin th) (taylor 0 kx) (#s(alt (.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)) (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 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (.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)) (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 (+ (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))))))))))) (taylor 0 kx) (#s(alt (.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)) (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 (+ (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)))))))))))) (taylor 0 kx) (#s(alt (.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)) (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 1 (taylor 0 kx) (#s(alt (/.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))))) (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 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (/.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))))) (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 (+ 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)))))) (taylor 0 kx) (#s(alt (/.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))))) (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 (+ 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)))))) (taylor 0 kx) (#s(alt (/.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))))) (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 (pow kx 2) (taylor 0 kx) (#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (taylor 0 kx) (#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (taylor 0 kx) (#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) (taylor 0 kx) (#s(alt (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor inf kx) (#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (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 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (/.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))))) (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 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (/.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))))) (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 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (/.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))))) (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 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (taylor -inf ky) (#s(alt (/.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))))) (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 (sin ky) (taylor -inf ky) (#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt (sin ky) (taylor -inf ky) (#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt (sin ky) (taylor -inf ky) (#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt (sin ky) (taylor -inf ky) (#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	ky	@	-inf	((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)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
4.0ms	th	@	0	((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)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
4.0ms	ky	@	0	((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)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	kx	@	inf	((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)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	kx	@	0	((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)))) (sin ky) (pow (sin ky) 2) (pow (sin kx) 2))

simplify218.0ms (1.9%)

Memory

8.6MiB live, 158.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 278×	`lower-fma.f64`
14 278×	`lower-fma.f32`
6 260×	`lower-*.f64`
6 260×	`lower-*.f32`
5 352×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	2263
1	1011	2214
2	3855	2122
3	7801	2122
0	8104	1974

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 119

Calls

Call 1

Inputs
(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))))))
(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))))
(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)))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 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)))))
(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))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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) (* 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))))
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))))
(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))))
(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)
(sin ky)
(sin ky)
(sin ky)
(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)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)

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

rewrite233.0ms (2.1%)

Memory

-8.4MiB live, 181.8MiB allocated

Rules

4 346×	`lower-fma.f64`
4 346×	`lower-fma.f32`
3 626×	`lower-*.f32`
3 624×	`lower-*.f64`
2 248×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	22	49
1	62	49
2	338	49
3	2902	49
0	8284	34

Stop Event

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

Counts

6 → 294

Calls

Call 1

Inputs
(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)))))
(sin.f64 ky)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Outputs
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))))
(.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))) #s(literal 3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64))) (pow.f64 (sin.f64 kx) #s(literal 8 binary64)))))
(.f64 (sqrt.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (+.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (+.f64 (sin.f64 ky) (sin.f64 kx))))
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(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(exp.f64 (-.f64 (neg.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))) (neg.f64 (log.f64 (sin.f64 ky)))))
(exp.f64 (-.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (neg.f64 (log.f64 (sin.f64 ky)))))
(exp.f64 (-.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64)) (neg.f64 (log.f64 (sin.f64 ky)))))
(exp.f64 (neg.f64 (log.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))))
(exp.f64 (+.f64 (neg.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))) (log.f64 (sin.f64 ky))))
(exp.f64 (fma.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64) (log.f64 (sin.f64 ky))))
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (neg.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)))))
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (.f64 (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64)) #s(literal -1 binary64))))
(exp.f64 (+.f64 (log.f64 (sin.f64 ky)) (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal -1/2 binary64))))
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (sqrt.f64 (sin.f64 ky))))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) (pow.f64 #s(literal 1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (sin.f64 ky)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 ky)))
(*.f64 #s(literal 1 binary64) (sin.f64 ky))
(*.f64 (sin.f64 ky) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (*.f64 (log.f64 (sin.f64 ky)) #s(literal 1/2 binary64)))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 ky)) #s(literal -1 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
(neg.f64 (neg.f64 (sin.f64 ky)))
(sin.f64 ky)
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 ky)))
(exp.f64 (neg.f64 (neg.f64 (log.f64 (sin.f64 ky)))))
(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 ky))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 ky)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (sin.f64 ky) #s(literal 3/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (sin.f64 ky)) #s(literal 2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)))
(*.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 ky)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (sin.f64 ky) (sin.f64 ky))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 ky)))
(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 ky ky))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 ky ky)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 ky ky)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 ky)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 ky))))
(exp.f64 (*.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 ky ky))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(*.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)) (sqrt.f64 (sin.f64 kx)))
(*.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) (sqrt.f64 (sin.f64 kx)))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (sin.f64 kx)) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(*.f64 (sin.f64 kx) (sin.f64 kx))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sin.f64 kx)))
(pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64))
(pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (exp.f64 (log1p.f64 (neg.f64 (cos.f64 (+.f64 kx kx))))) (exp.f64 (log.f64 #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (+.f64 kx kx)) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 1/2 binary64)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 kx))))
(exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))
(+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 kx kx))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))

eval123.0ms (1.1%)

Memory: 4.8MiB live, 102.2MiB allocated
Compiler: Compiled 12 851 to 1 668 computations (87% saved)

prune43.0ms (0.4%)

Memory

-4.6MiB live, 71.8MiB allocated

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	421	27	448
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	422	27	449

Accuracy

100.0%

Counts

449 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.6%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
	78.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	78.5%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (.f64 (sin.f64 th) (sin.f64 ky))))
	78.7%	(.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky))
	72.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	78.7%	(.f64 (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))) (sin.f64 th))
▶	78.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	44.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	67.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	51.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	35.2%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	78.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
	52.2%	(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64))) (sin.f64 th))
	78.6%	(.f64 (.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal -1/4 binary64))) (sin.f64 th))
	78.7%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	52.3%	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))) (sin.f64 th))
▶	78.6%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	20.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
	32.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	26.4%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 (fma.f64 (-.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 ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)) (sin.f64 th))
▶	26.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
	48.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
	48.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	93.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky))))
▶	28.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 1 364 to 874 computations (35.9% saved)

simplify145.0ms (1.3%)

Memory

-5.9MiB live, 118.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
cost-diff	0	(.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky)
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
cost-diff	7232	(fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))))
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
cost-diff	192	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
cost-diff	256	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
cost-diff	384	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
cost-diff	384	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
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	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Rules

5 188×	`lower-fma.f32`
5 182×	`lower-fma.f64`
4 344×	`lower-*.f32`
4 326×	`lower-*.f64`
1 866×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	476
0	88	454
1	138	453
2	267	444
3	700	429
4	1824	429
5	3503	420
6	7160	420
0	8055	406

Stop Event

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

Calls

Call 1

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

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

localize456.0ms (4.1%)

Memory

2.5MiB live, 351.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	1.4692769775790622	(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))
accuracy	1.8522466350180717	(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
accuracy	7.032326155651807	(.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
accuracy	43.72746421188797	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
accuracy	0.33203125	(.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
accuracy	3.3997881767730727	(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	15.916150238716815	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
accuracy	0.1875	(/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
accuracy	3.3997881767730727	(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	15.916150238716815	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
accuracy	0	(sin.f64 th)
accuracy	46.03562835145057	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0.0078125	(sin.f64 ky)
accuracy	0.05859375	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.140625	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
accuracy	0.1875	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Samples

221.0ms	93×	2	valid
113.0ms	88×	1	valid
36.0ms	75×	0	valid

Compiler

Compiled 483 to 50 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 263.0ms

adjust: 69.0ms (26.3% of total)

ival-cos: 33.0ms (12.6% of total)

ival-mult: 31.0ms (11.8% of total)

ival-hypot: 29.0ms (11% of total)

ival-sin: 26.0ms (9.9% of total)

ival-div: 25.0ms (9.5% of total)

ival-pow2: 17.0ms (6.5% of total)

ival-add: 9.0ms (3.4% of total)

ival-sqrt: 6.0ms (2.3% of total)

const: 5.0ms (1.9% of total)

ival-pow: 5.0ms (1.9% of total)

ival-sub: 4.0ms (1.5% of total)

ival-neg: 2.0ms (0.8% of total)

exact: 1.0ms (0.4% of total)

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

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

series171.0ms (1.5%)

Memory

-5.8MiB live, 194.7MiB allocated

Counts

21 → 564

Calls

Call 1

Inputs
#s(alt (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))) (patch (.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)) (patch (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) (patch (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky)) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky) (patch (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky) #<representation binary64>) () ())
#s(alt (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (patch (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (patch (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (patch (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) #<representation binary64>) () ())

Outputs
#s(alt (sin th) (taylor 0 kx) (#s(alt (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (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))))))))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))))))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 kx) (#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ 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)))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ 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)))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (sin ky) (taylor 0 kx) (#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky)))) (taylor 0 kx) (#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))) (taylor 0 kx) (#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))) (taylor 0 kx) (#s(alt (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (patch (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (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))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))) (taylor -inf ky) (#s(alt (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (patch (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))) (taylor -inf ky) (#s(alt (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (patch (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))) (taylor -inf ky) (#s(alt (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (patch (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
54.0ms	ky	@	inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (neg (sin ky)) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th))) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (/ (sin th) (pow (sin kx) 3)) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))))
15.0ms	kx	@	inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (neg (sin ky)) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th))) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (/ (sin th) (pow (sin kx) 3)) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))))
12.0ms	th	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (neg (sin ky)) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th))) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (/ (sin th) (pow (sin kx) 3)) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))))
11.0ms	kx	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (neg (sin ky)) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th))) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (/ (sin th) (pow (sin kx) 3)) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))))
10.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (neg (sin ky)) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th))) (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (/ (sin th) (pow (sin kx) 3)) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))))

simplify214.0ms (1.9%)

Memory

13.6MiB live, 280.0MiB allocated

Algorithm

1×	egg-herbie

Rules

9 532×	`lower-fma.f64`
9 532×	`lower-fma.f32`
7 448×	`lower-+.f64`
7 448×	`lower-+.f32`
7 054×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1058	16343
1	3555	15692
0	8270	15050

Stop Event

1×	iter limit
1×	node limit

Counts

564 → 562

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))))))))))))
(* 1/2 (- 1 (cos (* 2 ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(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))))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 2 (* (/ (* (pow kx 2) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* -1/2 (/ (* (pow ky 2) (sin th)) (pow kx 3)))
(/ (+ (* -1/2 (* (pow ky 2) (sin th))) (* (pow kx 2) (+ (* -1/4 (* (pow ky 2) (sin th))) (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))) (pow kx 3))
(/ (+ (* -1/2 (* (pow ky 2) (sin th))) (* (pow kx 2) (+ (* -1/4 (* (pow ky 2) (sin th))) (+ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (* (pow kx 2) (- (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))))))) (pow kx 3))
(/ (+ (* -1/2 (* (pow ky 2) (sin th))) (* (pow kx 2) (+ (* -1/4 (* (pow ky 2) (sin th))) (+ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (* (pow kx 2) (- (+ (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th))))) (* (pow kx 2) (- (* 1/2 (+ (* -41/3024 (* (pow ky 2) (sin th))) (+ (* 13/240 (* (pow ky 2) (sin th))) (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th)))))))) (+ (* -1/36 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))))))) (pow kx 3))
(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))))))))))))
(* -1/2 (/ (* (pow ky 3) (sin th)) (pow kx 3)))
(/ (+ (* -1/2 (* (pow ky 3) (sin th))) (* (pow kx 2) (* ky (+ (* -1/4 (* (pow ky 2) (sin th))) (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))) (pow kx 3))
(/ (+ (* -1/2 (* (pow ky 3) (sin th))) (* (pow kx 2) (+ (* ky (+ (* -1/4 (* (pow ky 2) (sin th))) (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))) (* (pow kx 2) (* ky (- (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))))))) (pow kx 3))
(/ (+ (* -1/2 (* (pow ky 3) (sin th))) (* (pow kx 2) (+ (* ky (+ (* -1/4 (* (pow ky 2) (sin th))) (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))) (* (pow kx 2) (+ (* ky (- (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))) (* (pow kx 2) (* ky (- (* 1/2 (+ (* -41/3024 (* (pow ky 2) (sin th))) (+ (* 13/240 (* (pow ky 2) (sin th))) (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th)))))))) (+ (* -1/36 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))))))))) (pow kx 3))
(/ (* (pow ky 2) (sin th)) (pow kx 3))
(/ (+ (* 1/2 (* (pow kx 2) (* (pow ky 2) (sin th)))) (* (pow ky 2) (sin th))) (pow kx 3))
(/ (+ (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th)))))) (* -1/2 (* (pow ky 2) (sin th))))) (* (pow ky 2) (sin th))) (pow kx 3))
(/ (+ (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -41/3024 (* (pow ky 2) (sin th))) (+ (* 13/240 (* (pow ky 2) (sin th))) (* 1/2 (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th))))))))) (+ (* -1/4 (* (pow ky 2) (sin th))) (* 13/120 (* (pow ky 2) (sin th)))))) (* -1/2 (* (pow ky 2) (sin th))))) (* (pow ky 2) (sin th))) (pow kx 3))
(* 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) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (* (/ (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(/ (sin th) (pow kx 3))
(/ (+ (sin th) (* 1/2 (* (pow kx 2) (sin th)))) (pow kx 3))
(/ (+ (sin th) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/4 (sin th)) (* 13/120 (sin th))))) (* -1/2 (sin th))))) (pow kx 3))
(/ (+ (sin th) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -41/3024 (sin th)) (+ (* 13/240 (sin th)) (* 1/2 (+ (* -1/4 (sin th)) (* 13/120 (sin th)))))))) (+ (* -1/4 (sin th)) (* 13/120 (sin th))))) (* -1/2 (sin th))))) (pow kx 3))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) kx)
(/ (+ (* 1/6 (* (pow kx 2) (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))) (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) kx)
(/ (+ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))) kx)
(/ (+ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (+ (* 1/720 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/6 (+ (* -1/36 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))))))))) (+ (* -1/36 (* (sin th) (+ 1 (* -1/6 (pow ky 2))))) (* 1/120 (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))) (* -1/6 (* (sin th) (+ 1 (* -1/6 (pow ky 2)))))))) 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)))))
(* (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)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* (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)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))
(* 1/2 (- 1 (cos (neg (* -2 kx)))))
(* 1/2 (- 1 (cos (neg (* -2 kx)))))
(* 1/2 (- 1 (cos (neg (* -2 kx)))))
(* 1/2 (- 1 (cos (neg (* -2 kx)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(- 1 (cos (neg (* -2 kx))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(* (* 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 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* -1 (* th (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* 1/6 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/6 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))))
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* 1/6 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/120 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* 1/5040 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))))) (/ 1 (sin kx))))))
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (+ (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))))) (/ 1 (sin kx))))))
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (+ (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/10080 (/ (pow ky 2) (pow (sin kx) 3))))))))))) (/ 1 (sin kx))))))
(* (* 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))))))))))))
(* ky (* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))))
(* th (+ (* ky (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3)))))) (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))))
(* th (+ (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))) (* (pow th 2) (+ (* ky (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))) (* ky (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3)))))))))
(* th (+ (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))) (* (pow th 2) (+ (* ky (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))))) (* (pow th 2) (+ (* ky (* (pow th 2) (+ (* -1/5040 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/10080 (/ (pow ky 2) (pow (sin kx) 3)))))) (* ky (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))))))))
(/ (* (pow ky 2) th) (pow (sin kx) 3))
(* th (+ (* -1/6 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))) (/ (pow ky 2) (pow (sin kx) 3))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))))) (/ (pow ky 2) (pow (sin kx) 3))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))) (* 1/120 (/ (pow ky 2) (pow (sin kx) 3))))))) (/ (pow ky 2) (pow (sin kx) 3))))
(/ th (pow (sin kx) 3))
(* th (+ (* -1/6 (/ (pow th 2) (pow (sin kx) 3))) (/ 1 (pow (sin kx) 3))))
(* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (pow (sin kx) 3))) (* 1/6 (/ 1 (pow (sin kx) 3))))) (/ 1 (pow (sin kx) 3))))
(* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (pow (sin kx) 3))) (* 1/120 (/ 1 (pow (sin kx) 3))))) (* 1/6 (/ 1 (pow (sin kx) 3))))) (/ 1 (pow (sin kx) 3))))
(/ (* th (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(* th (+ (* -1/6 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))
(* th (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/120 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))) (/ 1 (sin kx)))))
(* th (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))))))) (/ 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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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)))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (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))))
(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))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ (* (pow ky 2) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (/ (* (pow ky 2) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))))))))
(/ (sin th) (sin kx))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (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 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))))) (/ (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))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(/ (sin th) (sin kx))
(+ (* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx))) (/ (sin th) (sin kx)))
(+ (* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx))) (/ (sin th) (sin kx)))
(+ (* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx))) (/ (sin th) (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)))))
(* (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)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (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)))))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx)))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (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)))))
(* (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)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (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)))))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx)))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))

Outputs
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(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))
(+ (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)))))))))))
(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))
(+ (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))))))))))))
(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 #s(literal -1/2 binary64) (.f64 kx kx)) (.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 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 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))))))
(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))
(+ 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))))))
(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 #s(literal -1/2 binary64) (.f64 kx kx)) (.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 ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 (*.f64 kx kx) (sin.f64 ky)) #s(literal 1/2 binary64) (sin.f64 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))))))
(fma.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (.f64 kx kx)) (sin.f64 ky)) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (*.f64 kx kx) (sin.f64 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))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 kx kx) (/.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 ky))) (.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(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))
(+ (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)))))))))))
(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))
(+ (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))))))))))))
(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 #s(literal -1/2 binary64) (.f64 kx kx)) (.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 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(* 1/2 (- 1 (cos (* 2 ky))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx)))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(.f64 (fma.f64 (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) #s(literal 1 binary64)) (*.f64 kx kx))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky)))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(fma.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (.f64 kx kx)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(- 1 (cos (neg (* -2 kx))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (*.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (*.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* -1 (* th (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* 1/6 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/6 binary64) (.f64 th th) #s(literal -1 binary64))) th)
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/120 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/6 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal -1/120 binary64) (.f64 th th) #s(literal 1/6 binary64))) (.f64 th th) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) th)
(* th (+ (* -1 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* 1/6 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/120 (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* 1/5040 (* (pow th 2) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/5040 binary64) (.f64 th th) #s(literal -1/120 binary64))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #s(literal 1/6 binary64))) (.f64 th th) (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) th)
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))
(.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))))) (/ 1 (sin kx))))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx))))) th)
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (+ (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))))) (/ 1 (sin kx))))))
(.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/240 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/120 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx)))) (.f64 th th) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx))))) th)
(* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (+ (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/10080 (/ (pow ky 2) (pow (sin kx) 3))))))))))) (/ 1 (sin kx))))))
(.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/5040 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 #s(literal -1/240 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/120 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx)))) (.f64 th th) (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx)))) (.f64 th th) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx))))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* ky (* th (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))))
(.f64 (.f64 ky th) (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
(* th (+ (* ky (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3)))))) (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))))
(.f64 (.f64 ky (fma.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))) th)
(* th (+ (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))) (* (pow th 2) (+ (* ky (* (pow th 2) (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))) (* ky (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3)))))))))
(.f64 (fma.f64 (.f64 ky (fma.f64 (fma.f64 #s(literal -1/240 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/120 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))))) (.f64 th th) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) ky)) th)
(* th (+ (* ky (+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx))))) (* (pow th 2) (+ (* ky (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/12 (/ (pow ky 2) (pow (sin kx) 3))))) (* (pow th 2) (+ (* ky (* (pow th 2) (+ (* -1/5040 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/10080 (/ (pow ky 2) (pow (sin kx) 3)))))) (* ky (+ (* -1/240 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx)))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 ky (fma.f64 (fma.f64 #s(literal 1/10080 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/5040 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 #s(literal -1/240 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/120 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))))) (.f64 th th) (.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) ky)) (.f64 th th) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) ky)) th)
(/ (* (pow ky 2) th) (pow (sin kx) 3))
(.f64 (.f64 ky ky) (/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
(* th (+ (* -1/6 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))) (/ (pow ky 2) (pow (sin kx) 3))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 th ky) (.f64 th ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/6 binary64) (/.f64 (*.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (pow ky 2) (pow (sin kx) 3))) (* 1/120 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))))) (/ (pow ky 2) (pow (sin kx) 3))))
(.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 th ky) (.f64 th ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal 1/120 binary64) (/.f64 (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 th th) (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(* th (+ (* (pow th 2) (+ (* -1/6 (/ (pow ky 2) (pow (sin kx) 3))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow ky 2) (pow th 2)) (pow (sin kx) 3))) (* 1/120 (/ (pow ky 2) (pow (sin kx) 3))))))) (/ (pow ky 2) (pow (sin kx) 3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 (.f64 th ky) (.f64 th ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/5040 binary64) (/.f64 (.f64 #s(literal 1/120 binary64) (.f64 ky ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 th th) (/.f64 (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 th th) (/.f64 (*.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(/ th (pow (sin kx) 3))
(/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(* th (+ (* -1/6 (/ (pow th 2) (pow (sin kx) 3))) (/ 1 (pow (sin kx) 3))))
(.f64 (fma.f64 (/.f64 (.f64 th th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (pow (sin kx) 3))) (* 1/6 (/ 1 (pow (sin kx) 3))))) (/ 1 (pow (sin kx) 3))))
(.f64 (fma.f64 (fma.f64 (/.f64 (.f64 th th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal 1/120 binary64) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 th th) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (pow (sin kx) 3))) (* 1/120 (/ 1 (pow (sin kx) 3))))) (* 1/6 (/ 1 (pow (sin kx) 3))))) (/ 1 (pow (sin kx) 3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 th th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/5040 binary64) (/.f64 #s(literal 1/120 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 th th) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 th th) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) th)
(/ (* th (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) th) (sin.f64 kx))
(* th (+ (* -1/6 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))) (+ (* -1/6 (/ (pow ky 2) (sin kx))) (/ 1 (sin kx)))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (fma.f64 (.f64 th th) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 kx)) (/.f64 (.f64 ky ky) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) th)
(* th (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* 1/120 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))) (/ 1 (sin kx)))))
(.f64 (fma.f64 (fma.f64 (.f64 (.f64 th th) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 kx))) #s(literal 1/120 binary64) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 (/.f64 (.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)
(* th (+ (* -1/6 (/ (pow ky 2) (sin kx))) (+ (* (pow th 2) (+ (* -1/6 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (* (pow th 2) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))) (* 1/120 (/ (+ 1 (* -1/6 (pow ky 2))) (sin kx))))))) (/ 1 (sin kx)))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 th th) (/.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 kx))) #s(literal -1/5040 binary64) (/.f64 (.f64 #s(literal 1/120 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (/.f64 (.f64 #s(literal -1/6 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (sin.f64 kx))) (.f64 th th) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))
(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx)))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx)))
(fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
(.f64 (fma.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))) ky)
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (sin th) (pow (sin kx) 3))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* 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))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.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 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* 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))))
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(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (+.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 ky))) ky)
(* 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))))
(.f64 (fma.f64 (-.f64 (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.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 ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)
(* 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))))
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ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 ky ky) #s(literal -1/6 binary64)) (*.f64 ky ky) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 ky ky) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal 1/2 binary64) (sin.f64 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))))))
(fma.f64 (fma.f64 (/.f64 (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (.f64 ky ky)) (sin.f64 kx)) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 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))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (sin.f64 kx))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
(/ (* ky (sin th)) (sin kx))
(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* 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))))
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(* 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))))
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(* 1/2 (- 1 (cos (* 2 kx))))
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(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 ky ky))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.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)))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(.f64 (fma.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64))) #s(literal -2 binary64) (.f64 (.f64 #s(literal -1/6 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))))) (.f64 ky ky) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (sqrt.f64 #s(literal 2 binary64)))) ky)
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
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(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 2 (* (/ (* (pow ky 2) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))
(fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (.f64 (.f64 #s(literal 2 binary64) (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 3 binary64))))))
(+ (* -1 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* 2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))))
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(* 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))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* 2 (pow ky 2))
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(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
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(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
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(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
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(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (*.f64 (sin.f64 ky) (sin.f64 th)))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* -1 (* (sin th) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))))
(.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky))))) (.f64 ky ky))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky))))) (.f64 ky ky))
(* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx))))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky))))) (.f64 ky ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx)))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.f64 (.f64 ky ky) ky))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(.f64 (neg.f64 (.f64 (.f64 ky ky) ky)) (neg.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (*.f64 ky ky)))))))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(.f64 (neg.f64 (.f64 (.f64 ky ky) ky)) (neg.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (*.f64 ky ky)))))))
(* -1 (* (pow ky 3) (+ (* -1 (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (* -1 (/ (sin th) (* (pow ky 2) (sin kx)))))))
(.f64 (neg.f64 (.f64 (.f64 ky ky) ky)) (neg.f64 (fma.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (*.f64 ky ky)))))))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))
(/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
(* -1/6 (/ (* (pow ky 2) (sin th)) (sin kx)))
(.f64 (.f64 (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) #s(literal -1/6 binary64))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky)))) (.f64 ky ky))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky)))) (.f64 ky ky))
(* (pow ky 2) (+ (* -1/6 (/ (sin th) (sin kx))) (/ (sin th) (* (pow ky 2) (sin kx)))))
(.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (sin.f64 th) (.f64 (sin.f64 kx) (.f64 ky ky)))) (.f64 ky ky))

rewrite116.0ms (1%)

Memory

26.6MiB live, 108.6MiB allocated

Rules

1 002×	`lower-*.f32`
984×	`lower-*.f64`
882×	`lower-fma.f32`
876×	`lower-fma.f64`
742×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	317
0	88	298
1	306	297
0	2341	297

Stop Event

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

Counts

21 → 324

Calls

Call 1

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

Outputs
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))) (sin.f64 th)))
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 th)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)))
(/.f64 (.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)))
(/.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(/.f64 (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (.f64 (sin.f64 th) (sin.f64 ky))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))) (sin.f64 ky))
(.f64 #s(literal -1 binary64) (/.f64 (sin.f64 ky) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))))
(.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))))
(.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(pow.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)) #s(literal -1 binary64))
(/.f64 (.f64 (sin.f64 ky) #s(literal 1 binary64)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky))))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) (sin.f64 ky)))
(/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))))
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))) (/.f64 (sin.f64 ky) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))))
(*.f64 (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 1/2 binary64)))
(pow.f64 (sin.f64 ky) #s(literal 1 binary64))
(sin.f64 ky)
(exp.f64 (*.f64 (log.f64 (sin.f64 ky)) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))) (sqrt.f64 (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))) (-.f64 #s(literal 1/2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))
(sqrt.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 kx) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(hypot.f64 (sin.f64 ky) (sin.f64 ky))
(exp.f64 (.f64 (log.f64 (-.f64 #s(literal 1/2 binary64) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))))) #s(literal 1/2 binary64)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(sin.f64 th)
(*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))
(.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(*.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (neg.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (neg.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))
(/.f64 (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (pow.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (fma.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) #s(literal 1/8 binary64)))))
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(*.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal -3 binary64)))
(pow.f64 (/.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (sin.f64 th)) #s(literal -1 binary64))
(/.f64 (*.f64 (sin.f64 th) #s(literal 1 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(/.f64 (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64))) (pow.f64 (sin.f64 kx) #s(literal 3/2 binary64)))
(/.f64 (/.f64 (sin.f64 th) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)))) (sin.f64 kx))
(/.f64 (neg.f64 (neg.f64 (sin.f64 th))) (neg.f64 (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
(/.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (-.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (sin.f64 th))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (sin.f64 th)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)) (sin.f64 th)))
(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
(neg.f64 (/.f64 (sin.f64 th) (neg.f64 (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))
(.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))
(.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))
(.f64 (sin.f64 th) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64))))
(/.f64 (.f64 (neg.f64 (sin.f64 th)) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (neg.f64 (sin.f64 kx)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64))) (/.f64 (sin.f64 kx) (sin.f64 th)))
(/.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx))) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)))))
(/.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))) (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal -1 binary64)))
(/.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64))) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)))))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (neg.f64 (sin.f64 th))) (neg.f64 (sin.f64 kx)))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1 binary64)) (/.f64 (sin.f64 kx) (sin.f64 th)))
(/.f64 (neg.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th))) (neg.f64 (sin.f64 kx)))
(/.f64 (.f64 (neg.f64 (sin.f64 th)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))) (.f64 (neg.f64 (sin.f64 kx)) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64))))
(/.f64 (.f64 (neg.f64 (sin.f64 th)) (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64))) (.f64 (neg.f64 (sin.f64 kx)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky))))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))) (.f64 (/.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64))) (.f64 (/.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky))))))
(/.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))) (.f64 (sin.f64 kx) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64))))
(/.f64 (.f64 (sin.f64 th) (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64))) (.f64 (sin.f64 kx) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky))))))
(/.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) (neg.f64 (sin.f64 th))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64)) (neg.f64 (sin.f64 kx))))
(/.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64)) (/.f64 (sin.f64 kx) (sin.f64 th))))
(/.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) (sin.f64 th)) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal -1 binary64)) (sin.f64 kx)))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (neg.f64 (sin.f64 th))) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)))) (neg.f64 (sin.f64 kx))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)))) (/.f64 (sin.f64 kx) (sin.f64 th))))
(/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) #s(literal 1 binary64)) (sin.f64 th)) (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)))) (sin.f64 kx)))
(/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th)) (sin.f64 kx))
(/.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) (/.f64 (sin.f64 kx) (sin.f64 th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (sin.f64 th))))
(fma.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (sin.f64 th) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))))
(fma.f64 (neg.f64 (sin.f64 th)) (/.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 kx))) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))))
(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx)) (/.f64 (sin.f64 th) (sin.f64 kx)))
(fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 #s(literal -1/6 binary64) (.f64 ky ky)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1 binary64)))
(fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 #s(literal -1/6 binary64) (*.f64 ky ky))))
(fma.f64 #s(literal 1 binary64) (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))))
(fma.f64 (sin.f64 th) (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))))
(+.f64 (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))) (/.f64 (sin.f64 th) (sin.f64 kx)))
(+.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 #s(literal -1/6 binary64) (.f64 ky ky))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1 binary64)))
(+.f64 (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 #s(literal -1/6 binary64) (.f64 ky ky))))
(+.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (.f64 (.f64 #s(literal -1/6 binary64) (*.f64 ky ky)) (/.f64 (sin.f64 th) (sin.f64 kx))))

eval435.0ms (3.9%)

Memory: -125.8MiB live, 323.8MiB allocated
Compiler: Compiled 36 968 to 2 398 computations (93.5% saved)

prune86.0ms (0.8%)

Memory

-28.2MiB live, 208.4MiB allocated

Pruning

50 alts after pruning (46 fresh and 4 done)

	Pruned	Kept	Total
New	1 105	34	1 139
Fresh	10	12	22
Picked	1	4	5
Done	0	0	0
Total	1 116	50	1 166

Accuracy

100.0%

Counts

1 166 → 50

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.6%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
	19.9%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
	78.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	72.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	49.9%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	49.6%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
✓	78.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	67.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	51.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	31.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	35.2%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
	31.1%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	78.6%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
	52.2%	(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64))) (sin.f64 th))
▶	78.7%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	19.9%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
✓	78.6%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	45.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	32.9%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	32.9%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
	78.6%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	40.5%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	20.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
	32.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	31.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	27.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
▶	20.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	31.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	26.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
	12.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
	32.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
	17.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)) ky))
	12.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
✓	28.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	11.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
	15.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
▶	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
▶	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))))
	31.0%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
	27.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))

Compiler

Compiled 2 331 to 1 536 computations (34.1% saved)

simplify76.0ms (0.7%)

Memory

27.1MiB live, 70.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (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 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	128	(*.f64 #s(literal 2 binary64) kx)
cost-diff	128	(.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
cost-diff	192	(+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))
cost-diff	192	(/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))
cost-diff	0	(/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
cost-diff	0	(fma.f64 (/.f64 (*.f64 kx 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 ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
cost-diff	0	(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
cost-diff	0	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
cost-diff	320	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky))
cost-diff	384	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))

Rules

1 558×	`lower-fma.f32`
1 552×	`lower-fma.f64`
826×	`lower-*.f32`
800×	`lower-*.f64`
424×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	552
0	124	534
1	195	530
2	294	506
3	538	503
4	882	503
5	1299	503
6	1661	503
7	1886	503
8	1933	503
9	1951	503
10	1967	503
11	1975	503
0	1975	477

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize446.0ms (4%)

Memory

-31.0MiB live, 783.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.1875	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.25390625	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	3.3997881767730727	(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	33.35423198236744	#s(approx (pow (sin kx) 2) (*.f64 kx kx))
accuracy	3.4156924797839423	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
accuracy	15.916150238716815	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))
accuracy	31.813291098458812	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))))
accuracy	0.140625	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
accuracy	0.25390625	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	5.596146936332687	(/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
accuracy	48.85111358711279	#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.03125	(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
accuracy	0.07421875	(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy	31.967925054512435	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy	46.03562835145057	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
accuracy	0.328125	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky))
accuracy	3.3997881767730727	(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	15.916150238716815	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))

Samples

191.0ms	94×	2	valid
132.0ms	88×	1	valid
52.0ms	74×	0	valid

Compiler

Compiled 474 to 57 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 316.0ms

ival-cos: 82.0ms (25.9% of total)

ival-sin: 54.0ms (17.1% of total)

ival-div: 39.0ms (12.3% of total)

adjust: 39.0ms (12.3% of total)

ival-mult: 39.0ms (12.3% of total)

ival-add: 20.0ms (6.3% of total)

ival-sub: 9.0ms (2.8% of total)

ival-sqrt: 9.0ms (2.8% of total)

ival-hypot: 8.0ms (2.5% of total)

const: 8.0ms (2.5% of total)

ival-pow2: 7.0ms (2.2% of total)

exact: 1.0ms (0.3% of total)

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

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

series120.0ms (1.1%)

Memory

-1.0MiB live, 195.2MiB allocated

Counts

29 → 612

Calls

Call 1

Inputs
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (patch #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) #<representation binary64>) () ())
#s(alt (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) (patch (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (patch (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (patch (.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (patch #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64)) (patch (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (patch (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))) (patch (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))) #<representation binary64>) () ())
#s(alt (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) (patch (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (patch (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) kx) (patch (.f64 #s(literal 2 binary64) kx) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #<representation binary64>) () ())
#s(alt #s(approx (pow (sin kx) 2) (.f64 kx kx)) (patch #s(approx (pow (sin kx) 2) (.f64 kx kx)) #<representation binary64>) () ())

Outputs
#s(alt (* 1/2 (- 1 (cos (* 2 ky)))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2)) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (/ (* (pow kx 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))))) (taylor 0 kx) (#s(alt (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (patch (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (pow kx 2) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (taylor 0 kx) (#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (taylor 0 kx) (#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))) (taylor 0 kx) (#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))))) (taylor 0 kx) (#s(alt (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) (patch (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (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))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt (.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (patch (.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt (.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) (patch (.f64 #s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf ky) (#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (taylor -inf ky) (#s(alt (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (sin ky) 2) (taylor -inf ky) (#s(alt (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))) (taylor -inf ky) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))) (taylor -inf ky) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))) (taylor -inf ky) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) #<representation binary64>) () ())) ())
#s(alt (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))))) (taylor -inf ky) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
21.0ms	ky	@	inf	((+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (* (- 1 (cos (+ kx kx))) 1/2) (* (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (/ (* kx kx) (pow (sin ky) 2)) (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))) (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (* 2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin ky) 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (pow (sin kx) 2))
9.0ms	kx	@	inf	((+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (* (- 1 (cos (+ kx kx))) 1/2) (* (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (/ (* kx kx) (pow (sin ky) 2)) (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))) (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (* 2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin ky) 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (pow (sin kx) 2))
6.0ms	kx	@	-inf	((+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (* (- 1 (cos (+ kx kx))) 1/2) (* (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (/ (* kx kx) (pow (sin ky) 2)) (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))) (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (* 2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin ky) 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (pow (sin kx) 2))
6.0ms	ky	@	-inf	((+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (* (- 1 (cos (+ kx kx))) 1/2) (* (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (/ (* kx kx) (pow (sin ky) 2)) (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))) (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (* 2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin ky) 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (pow (sin kx) 2))
5.0ms	kx	@	0	((+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (* (- 1 (cos (+ kx kx))) 1/2) (* (* (/ 1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin ky)) (sin th)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (/ (* kx kx) (pow (sin ky) 2)) (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))) (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (* 2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin ky) 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (pow (sin kx) 2))

simplify280.0ms (2.5%)

Memory

11.5MiB live, 326.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 054×	`lower-fma.f64`
8 054×	`lower-fma.f32`
6 520×	`lower-*.f64`
6 520×	`lower-*.f32`
6 016×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	897	14576
1	2902	13865
2	7510	13856
0	8071	13389

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 609

Calls

Call 1

Inputs
(* 1/2 (- 1 (cos (* 2 ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(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 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 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))))))))))))
(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))))
(/ (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))
(/ 2 (- 1 (cos (* 2 ky))))
(+ (* -4 (/ (pow kx 2) (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 ky))))))
(- 1 (cos (* 2 ky)))
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky)))
(* 1/2 (- 1 (cos (* 2 ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(* 2 kx)
(* 2 kx)
(* 2 kx)
(* 2 kx)
(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))))))
(* 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) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (* (/ (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* 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 2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (sqrt (- 1 (cos (* 2 ky)))))))))))
(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))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 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) (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)))))
(/ (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))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 2 kx)
(* 2 kx)
(* 2 kx)
(* 2 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)))))
(* (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)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(- 1 (cos (* 2 kx)))
(- 1 (cos (* 2 kx)))
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(/ (pow kx 2) (pow (sin ky) 2))
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(pow (sin kx) 2)
(pow (sin kx) 2)
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(pow (sin kx) 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 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
(* 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
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
1
(+ 1 (* -1/6 (pow th 2)))
(+ 1 (* -1/6 (pow th 2)))
(+ 1 (* -1/6 (pow th 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))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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)
(* -1/6 (pow th 3))
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(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
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(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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)
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(sin th)
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(* -1/6 (pow th 3))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (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 (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))
(/ (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))
(/ 2 (- 1 (cos (* 2 kx))))
(+ (* -4 (/ (pow ky 2) (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
(- 1 (cos (* 2 kx)))
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(/ (* 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))))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 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))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(+ (* -1 (* (* (pow ky 2) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* (pow ky 2) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))))))
(+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (sqrt 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))))))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 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) (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))))
(/ (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))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 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)
(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)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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))))
(/ (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))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 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)
(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)))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))

Outputs
(* 1/2 (- 1 (cos (* 2 ky))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx)))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)))
(+ (* -2 (* (/ (* (pow kx 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(fma.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (sin.f64 ky) (.f64 kx kx)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(fma.f64 (fma.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (.f64 kx kx)) (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))))) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (/.f64 (.f64 #s(literal -2 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (+.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) #s(literal 2 binary64) (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))) (sin.f64 ky)) (/.f64 (.f64 kx kx) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 kx kx) (.f64 (/.f64 (.f64 #s(literal -2 binary64) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky))))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(.f64 (fma.f64 (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) #s(literal 1 binary64)) (*.f64 kx kx))
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(fma.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (.f64 kx kx)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))) (.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64))))) (/.f64 (.f64 kx kx) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))) (.f64 (.f64 #s(literal -2 binary64) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
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(sin th)
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1
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1
#s(literal 1 binary64)
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(/ (pow kx 2) (pow (sin ky) 2))
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(/ 2 (- 1 (cos (* 2 ky))))
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(+ (* -4 (/ (pow kx 2) (pow (- 1 (cos (* 2 ky))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 ky))))))
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(- 1 (cos (* 2 ky)))
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(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky)))
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(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky)))
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(* 1/2 (- 1 (cos (* 2 ky))))
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(* 2 kx)
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(* 2 kx)
(*.f64 kx #s(literal 2 binary64))
(sin th)
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(sin ky)
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(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
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(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
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(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky)))))
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(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
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(* 2 (pow kx 2))
(.f64 (.f64 kx kx) #s(literal 2 binary64))
(* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))
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(* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))
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(* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))
(- 1 (cos (* 2 kx)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(pow (sin kx) 2)
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin th)
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(sin th)
(sin.f64 th)
(* -1/6 (pow th 3))
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(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th))
(* -1/6 (pow th 2))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin th)
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(sin th)
(sin.f64 th)
(* -1/6 (pow th 3))
(.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(* -1/6 (pow th 2))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* 1/2 (- 1 (cos (* 2 kx))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.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)))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) ky))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* 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))))
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(* 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))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* 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))))
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(* 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))))
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(/ ky (sin kx))
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(* 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))))
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(* 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))))
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(* -1/2 (/ (pow kx 2) (pow ky 2)))
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(/ (pow kx 2) (pow ky 2))
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(/ (+ (* 1/3 (* (pow kx 2) (pow ky 2))) (pow kx 2)) (pow ky 2))
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(/ (+ (* (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))
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(/ 2 (- 1 (cos (* 2 kx))))
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(+ (* -4 (/ (pow ky 2) (pow (- 1 (cos (* 2 kx))) 2))) (* 2 (/ 1 (- 1 (cos (* 2 kx))))))
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(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx)))
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(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx)))
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(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
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(* 1/2 (- 1 (cos (* 2 kx))))
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(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
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(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.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)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* 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))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (.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 (.f64 (sin.f64 th) #s(literal 1/120 binary64)) (sin.f64 kx)))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* 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))))
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(/ ky (sin kx))
(/.f64 ky (sin.f64 kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 (+.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 ky))) ky)
(* 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))))
(fma.f64 (.f64 (-.f64 (.f64 (+.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.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 ky)) ky (/.f64 ky (sin.f64 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))))
(fma.f64 (.f64 (-.f64 (.f64 (+.f64 (fma.f64 (-.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (fma.f64 (/.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)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.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 #s(literal -1/12 binary64) (sin.f64 kx)) (+.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 (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/5040 binary64) (sin.f64 kx)))) (.f64 ky ky) (fma.f64 (.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (+.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 ky)) ky (/.f64 ky (sin.f64 kx)))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(.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)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(.f64 (fma.f64 (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)) (.f64 ky ky) #s(literal 1 binary64)) ky)
(sin kx)
(sin.f64 kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) (*.f64 ky ky) (sin.f64 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))))))
(fma.f64 (fma.f64 (.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (*.f64 ky ky) (sin.f64 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))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
(* 2 (pow ky 2))
(.f64 (.f64 ky ky) #s(literal 2 binary64))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -2/3 binary64) #s(literal 2 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 4/45 binary64) #s(literal -2/3 binary64)) (.f64 ky ky) #s(literal 2 binary64)) (.f64 ky ky))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) (.f64 ky ky) #s(literal -2/3 binary64)) (.f64 ky ky) #s(literal 2 binary64)) (*.f64 ky ky))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64)))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 ky ky)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (fma.f64 #s(literal -1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) #s(literal 1/3 binary64)) (.f64 ky (/.f64 ky (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 ky ky) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (fma.f64 #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 2/45 binary64) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) #s(literal 1/3 binary64)) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))) (.f64 ky (/.f64 ky (sqrt.f64 #s(literal 1/2 binary64))))) (/.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sqrt.f64 #s(literal 1/2 binary64))))) (.f64 ky ky) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))) (.f64 ky ky) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(.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))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(.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))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(.f64 (fma.f64 (fma.f64 (/.f64 (.f64 #s(literal -2 binary64) (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))) (.f64 ky ky) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (*.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))))) ky)
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (*.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
(/ (pow kx 2) (pow (sin ky) 2))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ (pow kx 2) (pow (sin ky) 2))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ (pow kx 2) (pow (sin ky) 2))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ (pow kx 2) (pow (sin ky) 2))
(*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))
(/ 2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(* 1/2 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))
(.f64 (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(pow (sin ky) 2)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt 2) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))

rewrite96.0ms (0.9%)

Memory

5.6MiB live, 125.7MiB allocated

Rules

964×	`lower-*.f32`
938×	`lower-*.f64`
896×	`lower-fma.f32`
890×	`lower-fma.f64`
844×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	77	419
0	124	400
1	408	400
0	2811	385

Stop Event

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

Counts

29 → 401

Calls

Call 1

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

Outputs
(.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))) (/.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 (fma.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)) (.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) (*.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))))))
(.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1 binary64)))
(*.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64)) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
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(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))))
(fma.f64 #s(literal -1 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(+.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))))
(+.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(pow.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal -1/2 binary64))))
(/.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (*.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
(sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))

eval189.0ms (1.7%)

Memory: 12.5MiB live, 319.0MiB allocated
Compiler: Compiled 32 465 to 2 881 computations (91.1% saved)

prune156.0ms (1.4%)

Memory

-9.4MiB live, 266.2MiB allocated

Pruning

75 alts after pruning (69 fresh and 6 done)

	Pruned	Kept	Total
New	1 074	37	1 111
Fresh	9	32	41
Picked	3	2	5
Done	0	4	4
Total	1 086	75	1 161

Accuracy

100.0%

Counts

1 161 → 75

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.6%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
	19.9%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
▶	78.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	72.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	49.9%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	49.6%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
✓	78.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	67.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	51.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	28.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
▶	31.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	35.2%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
	31.1%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	52.2%	(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64))) (sin.f64 th))
	31.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	33.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	32.9%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	31.1%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky)) (sin.f64 th))
	19.9%	(.f64 (.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
	19.9%	(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
	2.0%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
✓	78.6%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	32.9%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
	78.6%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	40.5%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	32.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	31.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	27.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
	21.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
	1.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	12.1%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
	15.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
	22.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	2.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
▶	31.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	12.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
	32.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
	17.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)) ky))
	12.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
✓	28.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	11.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
✓	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) th)))
	14.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
	13.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
▶	15.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
	10.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
	13.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
	31.0%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))
	27.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
	14.9%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
	23.5%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
	27.2%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
	22.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
	15.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
	19.3%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
▶	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
	15.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
	78.6%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky))))

Compiler

Compiled 3 509 to 2 180 computations (37.9% saved)

simplify69.0ms (0.6%)

Memory

4.6MiB live, 56.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
cost-diff	128	(*.f64 kx #s(literal 2 binary64))
cost-diff	128	(*.f64 ky #s(literal 2 binary64))
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
cost-diff	128	(*.f64 ky #s(literal 2 binary64))
cost-diff	128	(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))
cost-diff	0	(sin.f64 th)
cost-diff	0	(*.f64 ky (sin.f64 th))
cost-diff	0	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
cost-diff	0	#s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)
cost-diff	0	#s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
cost-diff	0	(sin.f64 th)
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
cost-diff	384	(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
cost-diff	384	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))

Rules

1 500×	`lower-fma.f32`
1 498×	`lower-fma.f64`
578×	`lower-*.f32`
558×	`lower-*.f64`
412×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	600
0	122	585
1	194	585
2	266	561
3	408	561
4	639	561
5	1023	561
6	1381	561
7	1566	561
8	1599	561
9	1616	561
10	1624	561
0	1624	532

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize413.0ms (3.7%)

Memory

-11.2MiB live, 616.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.9768068281132787	(.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))
accuracy	3.43144953963017	(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
accuracy	10.188542961187952	(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
accuracy	31.813291098458812	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
accuracy	0.1875	(/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))))
accuracy	3.3997881767730727	(sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
accuracy	36.07557480447305	#s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
accuracy	0	(sin.f64 kx)
accuracy	0.125	(*.f64 ky (sin.f64 th))
accuracy	0.9151020751850237	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
accuracy	43.16370493352715	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
accuracy	0.03125	(.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)
accuracy	31.967925054512435	#s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))
accuracy	32.6586841780374	#s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64))
accuracy	46.03562835145057	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
accuracy	0.20703125	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
accuracy	3.3997881767730727	(sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
accuracy	13.62732969437333	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	15.916150238716815	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))

Samples

191.0ms	108×	2	valid
108.0ms	73×	1	valid
44.0ms	74×	0	valid
3.0ms	1×	3	valid

Compiler

Compiled 458 to 59 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 292.0ms

ival-cos: 96.0ms (32.9% of total)

ival-sin: 46.0ms (15.8% of total)

ival-mult: 38.0ms (13% of total)

adjust: 33.0ms (11.3% of total)

ival-div: 19.0ms (6.5% of total)

ival-sub: 15.0ms (5.1% of total)

ival-sqrt: 14.0ms (4.8% of total)

ival-add: 12.0ms (4.1% of total)

ival-pow2: 12.0ms (4.1% of total)

const: 5.0ms (1.7% of total)

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

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

exact: 0.0ms (0% of total)

series80.0ms (0.7%)

Memory

33.6MiB live, 147.5MiB allocated

Counts

27 → 588

Calls

Call 1

Inputs
#s(alt (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)) (patch #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th) (patch (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) (patch #s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (patch (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) #<representation binary64>) () ())
#s(alt (.f64 ky (sin.f64 th)) (patch (.f64 ky (sin.f64 th)) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 ky #s(literal 2 binary64)) (patch (.f64 ky #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (.f64 kx #s(literal 2 binary64)) (patch (.f64 kx #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 ( 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (sin.f64 kx) (patch (sin.f64 kx) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) (patch (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) #<representation binary64>) () ())

Outputs
#s(alt (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt (+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt (+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky))))))))))) (taylor 0 kx) (#s(alt (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (- 1 (cos (* 2 ky)))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2)) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))) (taylor 0 kx) (#s(alt (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (patch (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow kx 2) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3)))) (taylor 0 kx) (#s(alt (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (patch (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (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))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))) #<representation binary64>) () ())) ())
#s(alt (sin th) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2)))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ (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))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (+ (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)))))))))))) (taylor 0 kx) (#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx))) (patch #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))) #<representation binary64>) () ())) ())
#s(alt (/ (* ky (sin th)) kx) (taylor 0 kx) (#s(alt (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (patch (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* 1/6 (* (pow kx 2) (* ky (sin th)))) (* ky (sin th))) kx) (taylor 0 kx) (#s(alt (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (patch (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* ky (sin th)) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th)))))) (* -1/6 (* ky (sin th)))))) kx) (taylor 0 kx) (#s(alt (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (patch (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) #<representation binary64>) () ())) ())
#s(alt (/ (+ (* ky (sin th)) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (* ky (sin th))) (+ (* 1/720 (* ky (sin th))) (* 1/6 (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th))))))))) (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th)))))) (* -1/6 (* ky (sin th)))))) kx) (taylor 0 kx) (#s(alt (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (patch (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) #<representation binary64>) () ())) ())
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#s(alt (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 ( 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))) (taylor -inf ky) (#s(alt (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) (patch (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 ( 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (neg (* -2 ky)))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))) (taylor -inf ky) (#s(alt #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))) (taylor -inf ky) (#s(alt #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))) (taylor -inf ky) (#s(alt #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))) (taylor -inf ky) (#s(alt #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 1 (cos (* 2 ky))) (taylor -inf ky) (#s(alt (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (patch (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))) (taylor -inf ky) (#s(alt (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (patch (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) (taylor -inf ky) (#s(alt (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) (patch (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) (taylor -inf ky) (#s(alt (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) (patch (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) (taylor -inf ky) (#s(alt (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) (patch (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))) (taylor -inf ky) (#s(alt (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) (patch (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))) (taylor -inf ky) (#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	ky	@	inf	((/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (* ky (sin th)) (sin kx)) (* ky (sin th)) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* kx 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin kx) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (- (- 2 (cos (* ky 2))) (cos (* kx 2))) (sqrt (/ 1 (- (- 2 (cos (* ky 2))) (cos (* kx 2))))))
6.0ms	th	@	0	((/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (* ky (sin th)) (sin kx)) (* ky (sin th)) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* kx 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin kx) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (- (- 2 (cos (* ky 2))) (cos (* kx 2))) (sqrt (/ 1 (- (- 2 (cos (* ky 2))) (cos (* kx 2))))))
6.0ms	ky	@	-inf	((/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (* ky (sin th)) (sin kx)) (* ky (sin th)) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* kx 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin kx) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (- (- 2 (cos (* ky 2))) (cos (* kx 2))) (sqrt (/ 1 (- (- 2 (cos (* ky 2))) (cos (* kx 2))))))
5.0ms	th	@	-inf	((/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (* ky (sin th)) (sin kx)) (* ky (sin th)) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* kx 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin kx) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (- (- 2 (cos (* ky 2))) (cos (* kx 2))) (sqrt (/ 1 (- (- 2 (cos (* ky 2))) (cos (* kx 2))))))
5.0ms	th	@	inf	((/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (* (- 1 (cos (+ kx kx))) 1/2) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (+ (* (* th th) -1/6) 1) th) (+ (* (* th th) -1/6) 1) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (* ky (sin th)) (sin kx)) (* ky (sin th)) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* kx 2) (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (- 1 (cos (+ kx kx))) (- 1 (cos (+ ky ky))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin kx) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (* ky 2))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (- (- 2 (cos (* ky 2))) (cos (* kx 2))) (sqrt (/ 1 (- (- 2 (cos (* ky 2))) (cos (* kx 2))))))

simplify283.0ms (2.5%)

Memory

8.1MiB live, 311.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 974×	`lower-fma.f64`
7 974×	`lower-fma.f32`
6 394×	`lower-*.f64`
6 394×	`lower-*.f32`
5 718×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	831	15232
1	2748	14290
2	6779	14124
0	8148	13781

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 584

Calls

Call 1

Inputs
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* 1/2 (- 1 (cos (* 2 ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(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))))
(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))))))))))))
(/ (* ky (sin th)) kx)
(/ (+ (* 1/6 (* (pow kx 2) (* ky (sin th)))) (* ky (sin th))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th)))))) (* -1/6 (* ky (sin th)))))) kx)
(/ (+ (* ky (sin th)) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (* ky (sin th))) (+ (* 1/720 (* ky (sin th))) (* 1/6 (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th))))))))) (+ (* -1/36 (* ky (sin th))) (* 1/120 (* ky (sin th)))))) (* -1/6 (* ky (sin th)))))) kx)
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (sin ky)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (sin ky) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* 2 kx)
(* 2 kx)
(* 2 kx)
(* 2 kx)
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(+ (* -1 (* (* (pow kx 2) (* th (* (sin ky) (sqrt 2)))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(+ (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -1 (* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* th (* (sin ky) (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky)))))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (* th (* (sin ky) (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))))) (sqrt (- 1 (cos (* 2 ky)))))))))))
(* 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) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (* (/ (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 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))))
(* 1/2 (- 1 (cos (* 2 ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (* (/ (pow kx 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* (pow kx 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))) (* 1/2 (* (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 ky)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))))))))
(- 1 (cos (* 2 ky)))
(- (+ 1 (* 2 (pow kx 2))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))) (cos (* 2 ky)))
(- (+ 1 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))) (cos (* 2 ky)))
(sqrt (/ 1 (- 1 (cos (* 2 ky)))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* -1 (* (pow kx 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1 (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 1/2 (* (* (pow kx 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (sqrt (- 1 (cos (* 2 ky)))))))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 ky))))) (* (pow kx 2) (+ (* -1 (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (- 1 (cos (* 2 ky))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))))))) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (sqrt (- 1 (cos (* 2 ky)))) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (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 (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
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(* 2 kx)
(* 2 kx)
(* 2 kx)
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(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
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(sin kx)
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(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
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(* 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
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
1
(+ 1 (* -1/6 (pow th 2)))
(+ 1 (* -1/6 (pow th 2)))
(+ 1 (* -1/6 (pow th 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))))))))))))
(/ (* ky th) (sin kx))
(* th (+ (* -1/6 (/ (* ky (pow th 2)) (sin kx))) (/ ky (sin kx))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ ky (sin kx))) (* 1/120 (/ (* ky (pow th 2)) (sin kx))))) (/ ky (sin kx))))
(* th (+ (* (pow th 2) (+ (* -1/6 (/ ky (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (* ky (pow th 2)) (sin kx))) (* 1/120 (/ ky (sin kx))))))) (/ ky (sin kx))))
(* ky th)
(* th (+ ky (* -1/6 (* ky (pow th 2)))))
(* th (+ ky (* (pow th 2) (+ (* -1/6 ky) (* 1/120 (* ky (pow th 2)))))))
(* th (+ ky (* (pow th 2) (+ (* -1/6 ky) (* (pow th 2) (+ (* -1/5040 (* ky (pow th 2))) (* 1/120 ky)))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(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)
(* -1/6 (pow th 3))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 3) (- (/ 1 (pow th 2)) 1/6))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (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 (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(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)
(* -1/6 (pow th 3))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1/6 (pow th 2))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (pow th 2) (- (/ 1 (pow th 2)) 1/6))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (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 (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(/ (* 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 th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(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))))
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* (* ky (* th (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(* ky (+ (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(* ky (+ (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
(* ky (+ (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (* th (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (* th (* (sqrt 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx)))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (* th (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/120 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(* 1/2 (- 1 (cos (* 2 kx))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(* 2 (pow ky 2))
(* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))
(* (pow ky 2) (+ 2 (* (pow ky 2) (- (* (pow ky 2) (+ 4/45 (* -2/315 (pow ky 2)))) 2/3))))
(* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))
(+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
(- 1 (cos (* 2 kx)))
(- (+ 1 (* 2 (pow ky 2))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* -2/3 (pow ky 2))))) (cos (* 2 kx)))
(- (+ 1 (* (pow ky 2) (+ 2 (* (pow ky 2) (- (* 4/45 (pow ky 2)) 2/3))))) (cos (* 2 kx)))
(sqrt (/ 1 (- 1 (cos (* 2 kx)))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* -1 (* (pow ky 2) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1 (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 1/2 (* (* (pow ky 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (sqrt (- 1 (cos (* 2 kx)))))))))
(+ (sqrt (/ 1 (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1 (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* (pow ky 2) (+ (* -1/2 (* (* (pow ky 2) (+ (* -1 (/ (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (- 1 (cos (* 2 kx))))) (+ (* 4/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))) (* 2 (/ (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))))))) (sqrt (- 1 (cos (* 2 kx)))))) (* 1/2 (* (sqrt (- 1 (cos (* 2 kx)))) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 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)))))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (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 (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(/ (* ky (sin th)) (sin kx))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* ky (sin th))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* 2 ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(- 1 (cos (neg (* -2 ky))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(- 1 (cos (* 2 ky)))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))

Outputs
(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky)))
(+ (* -2 (* (/ (* (pow kx 2) (* (sin ky) (sin th))) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))))
(fma.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (.f64 kx kx)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* 1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3)))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (.f64 kx kx) (sin.f64 ky)) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(+ (* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky)))))) (* (pow kx 2) (+ (* -2 (* (/ (* (sin ky) (sin th)) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (/ (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 ky)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (- 1 (cos (* 2 ky))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 3))))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))) (* 1/2 (* (/ (* (sin ky) (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 ky))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 ky))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 ky))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 ky)))))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) (fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (+.f64 (+.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) (/.f64 #s(literal 8/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (/.f64 #s(literal 8/45 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (/.f64 (.f64 kx kx) (sqrt.f64 #s(literal 2 binary64)))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (-.f64 (+.f64 (/.f64 #s(literal 8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64))) (/.f64 #s(literal 4/3 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64)))) (/.f64 #s(literal 2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))) (sin.f64 th)) (/.f64 (sin.f64 ky) (sqrt.f64 #s(literal 2 binary64))))))) (.f64 kx kx) (.f64 (.f64 #s(literal -2 binary64) (/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (pow kx 2))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (.f64 kx kx))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx)))
(+ (* 1/2 (- 1 (cos (* 2 ky)))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (.f64 (fma.f64 (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx)))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
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kx
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
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(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
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(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
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(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
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(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
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(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
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(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (sin.f64 ky))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)
th
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
(* th (+ 1 (* -1/6 (pow th 2))))
(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
1
#s(literal 1 binary64)
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1 (* -1/6 (pow th 2)))
(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* 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)))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* 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))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(* 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))))))))))))
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(/ (* ky th) (sin kx))
(*.f64 (/.f64 ky (sin.f64 kx)) th)
(* th (+ (* -1/6 (/ (* ky (pow th 2)) (sin kx))) (/ ky (sin kx))))
(.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) ky) (*.f64 th (/.f64 th (sin.f64 kx))) (/.f64 ky (sin.f64 kx))) th)
(* th (+ (* (pow th 2) (+ (* -1/6 (/ ky (sin kx))) (* 1/120 (/ (* ky (pow th 2)) (sin kx))))) (/ ky (sin kx))))
(.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/120 binary64) ky) (.f64 th (/.f64 th (sin.f64 kx))) (.f64 (/.f64 ky (sin.f64 kx)) #s(literal -1/6 binary64))) (*.f64 th th) (/.f64 ky (sin.f64 kx))) th)
(* th (+ (* (pow th 2) (+ (* -1/6 (/ ky (sin kx))) (* (pow th 2) (+ (* -1/5040 (/ (* ky (pow th 2)) (sin kx))) (* 1/120 (/ ky (sin kx))))))) (/ ky (sin kx))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/5040 binary64) ky) (.f64 th (/.f64 th (sin.f64 kx))) (.f64 (/.f64 ky (sin.f64 kx)) #s(literal 1/120 binary64))) (.f64 th th) (.f64 (/.f64 ky (sin.f64 kx)) #s(literal -1/6 binary64))) (*.f64 th th) (/.f64 ky (sin.f64 kx))) th)
(* ky th)
(*.f64 th ky)
(* th (+ ky (* -1/6 (* ky (pow th 2)))))
(.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)
(* th (+ ky (* (pow th 2) (+ (* -1/6 ky) (* 1/120 (* ky (pow th 2)))))))
(.f64 (fma.f64 (fma.f64 (.f64 (.f64 th th) ky) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) ky)) (*.f64 th th) ky) th)
(* th (+ ky (* (pow th 2) (+ (* -1/6 ky) (* (pow th 2) (+ (* -1/5040 (* ky (pow th 2))) (* 1/120 ky)))))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 th th) ky) #s(literal -1/5040 binary64) (.f64 #s(literal 1/120 binary64) ky)) (.f64 th th) (.f64 #s(literal -1/6 binary64) ky)) (*.f64 th th) ky) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 th th) (sin.f64 ky)) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 ky))) th)
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 #s(literal -1/5040 binary64) (.f64 (.f64 th th) (sin.f64 ky))))) (.f64 th th) (.f64 (.f64 #s(literal -1/6 binary64) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (sin.f64 ky))) th)
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
(.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky)))))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))))))
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(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* 1/2 (- 1 (cos (* 2 kx))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow ky 2))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (.f64 ky ky)))
(+ (* 1/2 (- 1 (cos (* 2 kx)))) (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))))
(fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.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)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(.f64 (fma.f64 (.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)
(* 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))))
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(* 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))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
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(* 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))))
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(* 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))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(pow ky 2)
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
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(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
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(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* 2 ky)
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(* 2 ky)
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))
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(* (* ky (* th (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
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(* ky (+ (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (neg.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/6 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))) (.f64 ky ky) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) ky)
(* ky (+ (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* th (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/6 (* (* th (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (* th (* (sqrt 2) (- (+ (* 2/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 4 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt (- 1 (cos (* 2 kx))))))))))))))
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(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
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(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* ky (sin th))
(*.f64 (sin.f64 th) ky)
(* 1/2 (- 1 (cos (* 2 ky))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))
(* 1/2 (- 1 (cos (* 2 ky))))
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(* 1/2 (- 1 (cos (* 2 ky))))
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(* 1/2 (- 1 (cos (* 2 ky))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))
(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* 2 ky)
(*.f64 #s(literal 2 binary64) ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
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(* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))) (sin.f64 ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))
(* (* th (* (sin ky) (sqrt 2))) (sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky)))))))
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(- 1 (cos (neg (* -2 ky))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
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(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
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(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
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(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))
(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
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(+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx)))))
(.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky))))))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
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(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
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(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
(- 1 (cos (* 2 ky)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 ky))))) (* 1/2 (- 1 (cos (* 2 kx))))))
(sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) ky)))))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
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(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))
(-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))
(sqrt (/ 1 (- 2 (+ (cos (* 2 kx)) (cos (* 2 ky))))))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))

rewrite86.0ms (0.8%)

Memory

13.1MiB live, 126.3MiB allocated

Rules

908×	`lower-*.f32`
896×	`lower-/.f32`
890×	`lower-*.f64`
886×	`lower-/.f64`
724×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	443
0	122	429
1	403	424
0	2661	410

Stop Event

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

Counts

27 → 282

Calls

Call 1

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

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

eval188.0ms (1.7%)

Memory: -1.4MiB live, 275.3MiB allocated
Compiler: Compiled 26 458 to 2 100 computations (92.1% saved)

prune143.0ms (1.3%)

Memory

31.1MiB live, 375.0MiB allocated

Pruning

100 alts after pruning (91 fresh and 9 done)

	Pruned	Kept	Total
New	881	40	921
Fresh	13	51	64
Picked	2	3	5
Done	0	6	6
Total	896	100	996

Accuracy

100.0%

Counts

996 → 100

Alt Table

Click to see full alt table

Status	Accuracy	Program
	78.6%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
	19.9%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
	32.9%	(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
✓	78.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.2%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
	31.0%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
	40.2%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	72.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	49.9%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	49.6%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
✓	78.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
	40.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	67.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	51.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	28.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	11.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (fma.f64 kx kx #s(literal 0 binary64))))) #s(literal 1/2 binary64))))) (sin.f64 th))
	11.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
	31.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
	11.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
	10.3%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
	15.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	11.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
	35.2%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	33.0%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
	31.1%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	33.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	52.2%	(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64))) (sin.f64 th))
	33.0%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	31.2%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	32.9%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
	31.1%	(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky)) (sin.f64 th))
	19.9%	(.f64 (.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
	19.9%	(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
	2.0%	(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
	33.0%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
	32.9%	(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
✓	78.6%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
	31.1%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
	78.6%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	40.5%	(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
	32.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	31.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
	27.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
	21.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
	1.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	12.1%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
	15.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
	22.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	2.5%	(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
	40.4%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))))))
	78.6%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky))))
	27.7%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
	31.0%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
✓	31.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	22.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
	22.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
	18.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
	18.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
	31.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
	32.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
	31.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (/.f64 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
	32.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
	12.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
	17.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)) ky))
✓	28.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	18.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
	11.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
✓	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	15.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
	14.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) th)))
	14.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
	13.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
✓	15.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
	10.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
	13.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
	14.9%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
	23.5%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
	27.2%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
	22.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
	15.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
	19.3%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
	23.6%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
	14.9%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx))))))))
	15.0%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)) th))
	16.8%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
	15.7%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
	40.4%	#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))))

Compiler

Compiled 5 206 to 2 016 computations (61.3% saved)

regimes450.0ms (4%)

Memory

-44.7MiB live, 767.8MiB allocated

Counts

139 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
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#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
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(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 (.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #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 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)) ky))
(.f64 (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 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)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 (fma.f64 (-.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 ky) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (/.f64 (sin.f64 ky) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 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))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (sin.f64 kx))) #s(literal 4 binary64)) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (exp.f64 #s(literal 1 binary64)) (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal -1/4 binary64))) (sin.f64 th))
(.f64 (.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 (sin.f64 ky))) #s(literal -1 binary64))) (sin.f64 th))

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

Calls

9 calls:

77.0ms	(sin.f64 ky)
54.0ms	(sin.f64 th)
50.0ms	(*.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))
44.0ms	(sin.f64 kx)
44.0ms	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 69 to 51 computations (26.1% saved)

regimes319.0ms (2.9%)

Memory

24.1MiB live, 451.3MiB allocated

Counts

126 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
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(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (fma.f64 kx kx #s(literal 0 binary64))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 (.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (.f64 (sin.f64 th) (sin.f64 ky))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))) (.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (sin.f64 th)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #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 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (fma.f64 (/.f64 (.f64 ky ky) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (*.f64 ky ky) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) th)) ky))
(.f64 (/.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))) (sin.f64 th))

Outputs

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

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

Calls

9 calls:

36.0ms	ky
36.0ms	(sin.f64 th)
35.0ms	(sin.f64 kx)
35.0ms	kx
35.0ms	th

Results

Accuracy	Segments	Branch
99.4%	2	`ky`
88.4%	2	`th`
94.2%	2	`kx`
88.0%	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%	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)))))`
99.5%	3	`(sin.f64 ky)`
94.2%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
94.2%	3	`(sin.f64 kx)`
88.2%	3	`(sin.f64 th)`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes326.0ms (2.9%)

Memory

32.3MiB live, 418.9MiB allocated

Counts

113 → 6

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
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(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (fma.f64 kx kx #s(literal 0 binary64))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))))
(.f64 (.f64 (sin.f64 th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64))))

Outputs
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th))

Calls

9 calls:

54.0ms	(sin.f64 ky)
38.0ms	(/.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)))))
35.0ms	kx
34.0ms	(sin.f64 kx)
32.0ms	th

Results

Accuracy	Segments	Branch
70.5%	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))`
72.4%	3	`(sin.f64 th)`
74.4%	3	`th`
72.2%	3	`(sin.f64 kx)`
71.7%	2	`kx`
71.7%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
84.9%	6	`(/.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)))))`
77.4%	3	`(sin.f64 ky)`
77.3%	2	`ky`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes212.0ms (1.9%)

Memory

-42.8MiB live, 325.1MiB allocated

Counts

105 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
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(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (fma.f64 kx kx #s(literal 0 binary64))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))

Outputs
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

6 calls:

31.0ms	th
31.0ms	kx
30.0ms	ky
29.0ms	(/.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)))))
29.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
67.6%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
67.9%	3	`kx`
60.1%	3	`th`
65.9%	4	`(sin.f64 ky)`
64.3%	3	`ky`
76.1%	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)))))`

Compiler

Compiled 40 to 30 computations (25% saved)

regimes35.0ms (0.3%)

Memory

33.4MiB live, 69.2MiB allocated

Counts

104 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))

Outputs
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Calls

1 calls:

28.0ms

(/.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
76.1%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes37.0ms (0.3%)

Memory

-4.1MiB live, 69.2MiB allocated

Counts

103 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
(*.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 ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)) th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx))))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (*.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (fma.f64 kx kx #s(literal 0 binary64))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (fma.f64 (.f64 (.f64 ky ky) #s(approx (/ (sin th) (pow (sin kx) 3)) (/.f64 (sin.f64 th) (.f64 (.f64 kx kx) kx)))) #s(literal -1/2 binary64) (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))) ky))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 kx kx #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 (*.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)) (/.f64 #s(literal 1 binary64) (fma.f64 ky ky #s(literal 0 binary64)))))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 kx kx #s(literal 0 binary64)) (.f64 (fma.f64 kx kx #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64))))) (sin.f64 th))

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

Calls

1 calls:

30.0ms

(/.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
76.1%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes95.0ms (0.9%)

Memory

-8.5MiB live, 64.6MiB allocated

Counts

93 → 5

Calls

Call 1

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

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

Calls

1 calls:

50.0ms

(/.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
76.1%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes33.0ms (0.3%)

Memory

12.7MiB live, 87.8MiB allocated

Counts

92 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
(*.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 ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)) th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx))))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) (sqrt.f64 #s(literal 2 binary64))) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))))))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))

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

Calls

1 calls:

25.0ms

(/.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
76.0%	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 16 to 11 computations (31.3% saved)

regimes31.0ms (0.3%)

Memory

-6.9MiB live, 77.6MiB allocated

Counts

78 → 5

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
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#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
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(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
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#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
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(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
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(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
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(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
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#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)) th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx))))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))) (sqrt.f64 #s(literal 1/2 binary64))))) (sin.f64 th))

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

Calls

1 calls:

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
76.0%	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 16 to 11 computations (31.3% saved)

regimes82.0ms (0.7%)

Memory

4.0MiB live, 121.6MiB allocated

Counts

73 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
(*.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 ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (sin.f64 ky) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx)))))) (sin.f64 ky)) th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 kx kx))) (cos.f64 (+.f64 kx kx))))))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))))) (sin.f64 th)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 th)))

Outputs

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

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

Calls

3 calls:

32.0ms	(sin.f64 th)
24.0ms	(sin.f64 kx)
20.0ms	(/.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
59.8%	4	`(sin.f64 kx)`
45.7%	4	`(sin.f64 th)`
68.3%	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)))))`

Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes112.0ms (1%)

Memory

6.4MiB live, 177.4MiB allocated

Counts

59 → 4

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
(*.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 ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))

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

Calls

6 calls:

22.0ms	ky
18.0ms	(/.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	(*.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))
17.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
16.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
58.0%	4	`(sin.f64 ky)`
51.6%	3	`ky`
49.9%	4	`(*.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))`
58.5%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
58.5%	3	`kx`
63.0%	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 55 to 40 computations (27.3% saved)

regimes20.0ms (0.2%)

Memory

-7.3MiB live, 30.4MiB allocated

Counts

57 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))
(*.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 ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (*.f64 kx kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))

Outputs

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

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

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

Calls

1 calls:

16.0ms

(/.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
60.5%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes31.0ms (0.3%)

Memory

-14.8MiB live, 22.9MiB allocated

Counts

54 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (.f64 (.f64 (sin.f64 th) ky) (sqrt.f64 #s(literal 2 binary64)))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (- (- 2 (cos ( ky 2))) (cos (* kx 2))) (-.f64 (fma.f64 (.f64 kx kx) #s(literal 2 binary64) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 2 binary64) ky)))))) (sqrt.f64 #s(literal 2 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) #s(approx (+ (- 1 (cos ( 2 kx))) (- 1 (cos (* ky 2)))) (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 4/45 binary64) (.f64 kx kx) #s(literal -2/3 binary64)) (.f64 kx kx) #s(literal 2 binary64)) (.f64 kx kx) #s(literal 1 binary64)) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 ky ky)) (sin.f64 th) (.f64 (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))) (.f64 kx kx))) (.f64 (*.f64 kx kx) kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (* (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) ky) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 ky ky) ky)) (sin.f64 th) (.f64 (.f64 (.f64 kx kx) ky) (.f64 (sin.f64 th) (fma.f64 #s(literal -1/4 binary64) (.f64 ky ky) (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)))))) (.f64 (*.f64 kx kx) kx))))

Outputs

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

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

Calls

1 calls:

14.0ms

(/.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
60.4%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes14.0ms (0.1%)

Memory

18.4MiB live, 18.4MiB allocated

Counts

42 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)))) (.f64 kx kx))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) #s(approx (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))))))

Outputs

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

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

Calls

1 calls:

11.0ms

(/.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
60.4%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes74.0ms (0.7%)

Memory

-1.9MiB live, 111.7MiB allocated

Counts

37 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sin.f64 th) (.f64 ky (/.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 #s(literal 1 binary64) (sin.f64 kx)) (.f64 ky (sin.f64 th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 kx) (*.f64 ky (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (* ky 2))) 1/2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 th) #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1 binary64))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 kx #s(literal 2 binary64)))))))))

Outputs

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

Calls

6 calls:

15.0ms	kx
13.0ms	(sin.f64 ky)
12.0ms	th
10.0ms	(sin.f64 kx)
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
49.0%	2	`(sin.f64 ky)`
50.0%	3	`(sin.f64 kx)`
45.8%	2	`kx`
45.8%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
37.8%	3	`th`
54.0%	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 41 to 31 computations (24.4% saved)

regimes11.0ms (0.1%)

Memory

26.6MiB live, 26.6MiB allocated

Counts

30 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (sin.f64 kx))) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) ky))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))

Outputs

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (*.f64 #s(approx (+ (* (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.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:

8.0ms

(/.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
54.0%	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 16 to 11 computations (31.3% saved)

regimes64.0ms (0.6%)

Memory

-33.4MiB live, 126.7MiB allocated

Counts

27 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (.f64 kx (/.f64 kx (.f64 ky ky)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (.f64 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (*.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (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))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) th) ky) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 (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)) (*.f64 kx kx) #s(literal 1 binary64)) kx))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 (/.f64 (.f64 kx 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))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (fma.f64 #s(approx (/ (* kx kx) (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (-.f64 (.f64 (.f64 kx kx) #s(literal 1/15 binary64)) (.f64 (fma.f64 (.f64 kx kx) #s(literal 11/945 binary64) (.f64 (.f64 (.f64 kx kx) #s(literal -1/15 binary64)) #s(literal 1/3 binary64))) (.f64 ky ky))) (.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))) (sin.f64 th))

Outputs

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

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

Calls

7 calls:

11.0ms	(*.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))
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)))))
9.0ms	(sin.f64 ky)
9.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
8.0ms	kx

Results

Accuracy	Segments	Branch
41.3%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
41.4%	3	`kx`
40.2%	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))`
41.7%	4	`(sin.f64 kx)`
42.9%	3	`(sin.f64 ky)`
42.6%	3	`ky`
44.6%	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 60 to 44 computations (26.7% saved)

regimes7.0ms (0.1%)

Memory

15.8MiB live, 15.8MiB allocated

Counts

19 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (*.f64 (sin.f64 th) ky) kx)))
(.f64 #s(approx (/ (sin ky) (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(approx (+ (* (/ (* kx kx) (pow (sin ky) 2)) -1/2) 1) (.f64 (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (*.f64 ky ky))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 (sin.f64 th) ky)) kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 #s(approx (* ky (sin th)) (.f64 (fma.f64 (.f64 (*.f64 th th) ky) #s(literal -1/6 binary64) ky) th)) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))) (sin.f64 kx)))

Outputs

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

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

Calls

1 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)))))

Results

Accuracy	Segments	Branch
44.4%	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 16 to 11 computations (31.3% saved)

regimes6.0ms (0.1%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

14 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) 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 (/ (* ky (sin th)) (sin kx)) (*.f64 (/.f64 ky (sin.f64 kx)) th)))

Outputs

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

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

Calls

1 calls:

5.0ms

(/.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
42.9%	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)))))`

Compiler

Compiled 16 to 11 computations (31.3% saved)

regimes39.0ms (0.4%)

Memory

4.1MiB live, 78.9MiB allocated

Counts

13 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Outputs

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

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

Calls

8 calls:

6.0ms	kx
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)))))
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 th)
4.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
32.9%	3	`(sin.f64 kx)`
37.1%	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))`
32.6%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
32.6%	2	`kx`
32.6%	2	`ky`
33.1%	2	`(sin.f64 ky)`
32.9%	3	`(sin.f64 th)`
37.1%	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)))))`

Compiler

Compiled 65 to 48 computations (26.2% saved)

regimes77.0ms (0.7%)

Memory

-2.0MiB live, 75.4MiB allocated

Counts

12 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) th) th #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th (*.f64 #s(literal 1 binary64) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (*.f64 th th) #s(literal 1 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (.f64 (.f64 th th) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal -1 binary64)))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th))) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 th th) (.f64 th th)) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 th th)))))) th)))

Outputs

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

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

Calls

9 calls:

39.0ms	kx
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)))))
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 kx)
4.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
21.9%	3	`(sin.f64 kx)`
20.1%	2	`(sin.f64 th)`
21.7%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
21.7%	2	`kx`
23.2%	2	`ky`
23.4%	2	`(sin.f64 ky)`
25.3%	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))`
20.1%	2	`th`
24.5%	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 69 to 51 computations (26.1% saved)

regimes40.0ms (0.4%)

Memory

-7.3MiB live, 30.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

9 calls:

29.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
1.0ms	(*.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))
1.0ms	(/.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)))))
1.0ms	(sin.f64 kx)
1.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
15.5%	1	`th`
15.5%	1	`(sin.f64 th)`
15.5%	1	`(sin.f64 kx)`
15.5%	1	`kx`
15.5%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
15.5%	1	`ky`
15.5%	1	`(sin.f64 ky)`
15.5%	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)))))`
15.5%	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))`

Compiler

Compiled 69 to 51 computations (26.1% saved)

bsearch28.0ms (0.3%)

Memory

13.1MiB live, 49.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
26.0ms	1.0835856851357735e-9	0.34607233264062026

Samples

20.0ms

144×

valid

Compiler

Compiled 463 to 324 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-sin: 11.0ms (66.9% of total)

ival-pow2: 2.0ms (12.2% of total)

ival-div: 1.0ms (6.1% of total)

ival-add: 1.0ms (6.1% of total)

ival-mult: 1.0ms (6.1% of total)

ival-sqrt: 1.0ms (6.1% of total)

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

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

bsearch1.0ms (0%)

Memory

2.4MiB live, 2.5MiB allocated

Algorithm

5×	left-value

Steps

Time	Left	Right
0.0ms	1.0	+inf
0.0ms	0.9972580999534978	1.0
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

2.0MiB live, 1.9MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9972580999534978	1.0
0.0ms	6.955696138239743e-24	3.3208587210691937e-23
0.0ms	-0.10444587622105783	1.492648709036486e-308
0.0ms	-0.9495956611663093	-0.9422676277152625

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch15.0ms (0.1%)

Memory

-39.1MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	-0.10444587622105783	1.492648709036486e-308

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	1.2395993825649923e-257	7.36946496070804e-255
0.0ms	-1.0	-0.9998527640017107

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	-1.0	-0.9998527640017107

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	-0.10444587622105783	1.492648709036486e-308

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293
0.0ms	-0.10444587622105783	1.492648709036486e-308

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.531514206621167e-8	0.12540248577476293

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch11.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	2.0842606821082576e-68	2.7659297895302443e-66

Samples

6.0ms

112×

valid

Compiler

Compiled 169 to 110 computations (34.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sin: 2.0ms (63% of total)

ival-mult: 1.0ms (31.5% of total)

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

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

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1e-323	7.277910673881339e-306

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify38.0ms (0.3%)

Memory

8.2MiB live, 43.6MiB allocated

Algorithm

1×	egg-herbie

Rules

164×	`unsub-neg_binary64`
124×	`*-commutative_binary64`
104×	`neg-mul-1_binary64`
70×	`sub-neg_binary64`
68×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	274	2996
1	348	2996
2	391	2996
3	434	2996
4	506	2996
5	545	2996
6	587	2996
7	671	2996
8	755	2996
9	768	2996

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (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 944473296573929/9444732965739290427392 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) 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 2 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) 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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) 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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (neg.f64 (sin.f64 ky)) #s(approx (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))) #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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) (.f64 (neg.f64 (sin.f64 ky)) #s(approx ( (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (neg.f64 (sin.f64 ky)) #s(approx (* (/ -1 (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (neg.f64 th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (+.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))))) #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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 kx #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))) #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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))) (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 6805647338418769/680564733841876926926749214863536422912 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) (cos.f64 (.f64 kx #s(literal 2 binary64))))))))) #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 -3602879701896397/36028797018963968 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky 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 944473296573929/9444732965739290427392 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 1352433999707303/67621699985365151533099492469314125634412457732623554832378970755414259527260782012725408753620120050518322559136912470896940487616343748768068989243256265844273495551872650773597634262582584454787101812251032115730947621472199902571314803042180668990660938354910463787008 binary64)) (.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))) (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 944473296573929/9444732965739290427392 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 944473296573929/9444732965739290427392 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))))) (.f64 (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) 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 944473296573929/9444732965739290427392 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2)))))) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64))))))))) (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 944473296573929/9444732965739290427392 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/9444732965739290427392 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/9444732965739290427392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 #s(approx (+ ( (* (* ky ky) (/ (sin th) (pow (sin kx) 3))) -1/2) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx)))) (/.f64 (sin.f64 th) (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 944473296573929/9444732965739290427392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 ky (sin.f64 th)) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) 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 944473296573929/9444732965739290427392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (/.f64 (.f64 (sin.f64 th) ky) 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 944473296573929/9444732965739290427392 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (/ (* ky (sin th)) (sin kx)) (.f64 (/.f64 ky (sin.f64 kx)) 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 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5767298273795133/60708402882054033466233184588234965832575213720379360039119137804340758912662765568 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/6 binary64))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (.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(literal 1/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (* (+ (* (* th th) -1/6) 1) th) (.f64 (.f64 (.f64 th th) th) #s(literal -1/6 binary64))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #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 -8511803295730237/9007199254740992 binary64)) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))))) (sin.f64 ky)) (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 -3602879701896397/36028797018963968 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (* 1/2 (+ (- 1 (cos (* 2 kx))) (- 1 (cos (* ky 2))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 2 binary64) (cos.f64 (+.f64 ky ky))) (cos.f64 (.f64 kx #s(literal 2 binary64)))))) (sqrt.f64 #s(literal 2 binary64)))))) (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 944473296573929/9444732965739290427392 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (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 8982502414685563/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 th th) #s(literal -1/6 binary64)) (.f64 th th) #s(literal 1 binary64)) 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 2 binary64)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64)) ky)) (sin.f64 kx))) (sin.f64 th)))))))
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#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)))

soundness1.8s (15.9%)

Memory

-64.2MiB live, 1 399.6MiB allocated

Rules

14 278×	`lower-fma.f64`
14 278×	`lower-fma.f32`
9 532×	`lower-fma.f64`
9 532×	`lower-fma.f32`
8 054×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	2263
1	1011	2214
2	3855	2122
3	7801	2122
0	8104	1974
0	13	49
0	22	49
1	62	49
2	338	49
3	2902	49
0	8284	34
0	831	15232
1	2748	14290
2	6779	14124
0	8148	13781
0	1058	16343
1	3555	15692
0	8270	15050
0	897	14576
1	2902	13865
2	7510	13856
0	8071	13389
0	82	443
0	122	429
1	403	424
0	2661	410

Stop Event

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

Compiler

Compiled 3 464 to 1 382 computations (60.1% saved)

preprocess203.0ms (1.8%)

Memory

15.6MiB live, 283.0MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 3 592 to 496 computations (86.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated