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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze207.0ms (1.7%)

Memory

-4.8MiB live, 467.8MiB 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)

sample1.6s (13.5%)

Memory

20.6MiB live, 2 467.6MiB allocated

Samples

1.3s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.0s

ival-sin: 633.0ms (61.6% of total)

ival-pow2: 178.0ms (17.3% of total)

ival-sqrt: 64.0ms (6.2% of total)

ival-mult: 55.0ms (5.4% of total)

ival-div: 50.0ms (4.9% of total)

ival-add: 36.0ms (3.5% of total)

ival-true: 7.0ms (0.7% of total)

ival-assert: 4.0ms (0.4% of total)

Bogosity

explain214.0ms (1.8%)

Memory

8.9MiB live, 285.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
10	-	1	(-3.703632751284704e-158 -2.461210150023734e-225 -4.867751719449685e-297)	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`
0	-	0	-	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`
0	-	0	-	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`
0	-	0	-	`(sin.f64 kx)`
0	-	0	-	`(sin.f64 th)`
0	-	0	-	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
0	-	0	-	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
0	-	0	-	`th`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
0	-	0	-	`(sin.f64 ky)`
0	-	0	-	`ky`
0	-	0	-	`kx`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))`	uflow-rescue	9	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	57
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	52
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	9

Confusion

	Predicted +	Predicted -
+	9	0
-	0	247

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	9	0	0
-	0	0	247

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	247
1	9

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

83.0ms

512×

valid

Compiler

Compiled 155 to 43 computations (72.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-sin: 34.0ms (58.1% of total)

ival-pow2: 10.0ms (17.1% of total)

ival-mult: 5.0ms (8.5% of total)

ival-sqrt: 4.0ms (6.8% of total)

ival-div: 3.0ms (5.1% of total)

ival-add: 2.0ms (3.4% of total)

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

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

exact: 0.0ms (0% of total)

preprocess72.0ms (0.6%)

Memory

9.2MiB live, 47.0MiB 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

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.2%	(*.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))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify4.0ms (0%)

Memory

5.2MiB live, 5.2MiB 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

localize53.0ms (0.4%)

Memory

-4.5MiB live, 72.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.171875	(/.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	0.2734375	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	0.29916000976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	2.317092876196292	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

41.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sin: 19.0ms (62% of total)

ival-pow2: 5.0ms (16.3% of total)

ival-mult: 2.0ms (6.5% of total)

ival-sqrt: 2.0ms (6.5% of total)

ival-div: 1.0ms (3.3% of total)

ival-add: 1.0ms (3.3% of total)

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

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

exact: 0.0ms (0% of total)

series41.0ms (0.3%)

Memory

-0.2MiB live, 49.4MiB 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
13.0ms	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))
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))
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))
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))

simplify187.0ms (1.6%)

Memory

9.2MiB live, 197.8MiB 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))

rewrite187.0ms (1.6%)

Memory

18.7MiB live, 171.0MiB 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))))

eval63.0ms (0.5%)

Memory: -6.9MiB live, 111.0MiB allocated
Compiler: Compiled 12 851 to 1 668 computations (87% saved)

prune139.0ms (1.2%)

Memory

6.4MiB live, 243.6MiB allocated

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	419	29	448
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	420	29	449

Accuracy

100.0%

Counts

449 → 29

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.1%	(/.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	79.2%	(/.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)))))
▶	79.2%	(/.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)))
	79.2%	(.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
	79.1%	(.f64 (/.f64 (sin.f64 th) (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))) (/.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))))
	79.3%	(.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))
	79.1%	(.f64 (/.f64 (sin.f64 ky) (pow.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)) #s(literal 2 binary64))) (sin.f64 th))
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	79.1%	(.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))
	79.3%	(.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))
	86.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th))
	45.2%	(.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))
	43.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	50.4%	(.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))
▶	35.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th))
	24.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	79.0%	(.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)))
	79.2%	(.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))
	54.5%	(.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))
	79.2%	(.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)))
	26.3%	(.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))
	21.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	17.7%	(.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))
	95.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (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.f64 th))
	26.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (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)))
▶	17.7%	#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))
	50.2%	#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)))))))
	92.9%	#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))))
▶	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 1 412 to 918 computations (35% saved)

simplify296.0ms (2.5%)

Memory

6.7MiB live, 84.9MiB 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	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)))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th))
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

4 972×	`lower-fma.f32`
4 964×	`lower-fma.f64`
3 452×	`lower-*.f32`
3 436×	`lower-*.f64`
1 298×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	426
0	91	397
1	141	397
2	251	393
3	601	383
4	1625	383
5	2902	374
6	3939	374
7	4574	374
8	4920	374
9	5053	374
10	5102	374
11	5128	374
12	5232	374
13	5340	374
14	5454	374
15	5557	374
16	5609	374
17	5609	374
18	5609	374
19	5609	374
20	5609	370
21	6236	370
22	6332	370
0	6332	362

Stop Event

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

localize337.0ms (2.8%)

Memory

-0.7MiB live, 587.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	2.8714770904177906	(/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))
accuracy	3.3779649612132037	(.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (sin.f64 kx)))
accuracy	8.517269499298207	(.f64 (.f64 ky ky) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
accuracy	50.821842520421484	#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	0.170253759768442	(/.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	2.317092876196292	(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	15.10509972035183	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
accuracy	15.22228271148396	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	0.11328125	(/.f64 kx (sin.f64 ky))
accuracy	0.16796875	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th))
accuracy	0.171875	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky))))
accuracy	44.99994331576801	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (*.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))
accuracy	0	(sin.f64 th)
accuracy	42.97460894060188	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.0234375	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.16796875	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
accuracy	0.171875	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Samples

135.0ms	96×	2	valid
77.0ms	86×	1	valid
41.0ms	74×	0	valid

Compiler

Compiled 396 to 49 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 198.0ms

ival-cos: 44.0ms (22.3% of total)

ival-sin: 30.0ms (15.2% of total)

ival-mult: 29.0ms (14.7% of total)

adjust: 21.0ms (10.6% of total)

ival-div: 19.0ms (9.6% of total)

ival-add: 12.0ms (6.1% of total)

ival-sub: 10.0ms (5.1% of total)

ival-sqrt: 8.0ms (4.1% of total)

ival-hypot: 7.0ms (3.5% of total)

ival-pow2: 7.0ms (3.5% of total)

ival-pow: 6.0ms (3% of total)

const: 5.0ms (2.5% of total)

exact: 1.0ms (0.5% of total)

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

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

series149.0ms (1.3%)

Memory

8.2MiB live, 163.4MiB allocated

Counts

23 → 588

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

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>) () ())) ())
#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)) (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) (taylor 0 kx) (#s(alt (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (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) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (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) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky)))) (sin.f64 th)) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (* 1/2 (- 1 (cos (* 2 ky))))) (taylor inf ky) (#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>) () ())) ())
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#s(alt (* (pow ky 3) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (taylor -inf ky) (#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 (* -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))))))) (taylor -inf ky) (#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 (* -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))))))) (taylor -inf ky) (#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 (* -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))))))) (taylor -inf ky) (#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 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3)) (taylor -inf ky) (#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 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3)) (taylor -inf ky) (#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 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3)) (taylor -inf ky) (#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 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3)) (taylor -inf ky) (#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 (/ kx (sin ky)) (taylor -inf ky) (#s(alt (/.f64 kx (sin.f64 ky)) (patch (/.f64 kx (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (/ kx (sin ky)) (taylor -inf ky) (#s(alt (/.f64 kx (sin.f64 ky)) (patch (/.f64 kx (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (/ kx (sin ky)) (taylor -inf ky) (#s(alt (/.f64 kx (sin.f64 ky)) (patch (/.f64 kx (sin.f64 ky)) #<representation binary64>) () ())) ())
#s(alt (/ kx (sin ky)) (taylor -inf ky) (#s(alt (/.f64 kx (sin.f64 ky)) (patch (/.f64 kx (sin.f64 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 (- 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 (* -1/6 (/ (* (pow ky 2) (sin th)) (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>) () ())) ())
#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
17.0ms	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) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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) (+ (* (* (* 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))) (sin kx) (/ kx (sin ky)) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))) (/ (sin th) (pow (sin kx) 3)))
13.0ms	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) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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) (+ (* (* (* 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))) (sin kx) (/ kx (sin ky)) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))) (/ (sin th) (pow (sin kx) 3)))
11.0ms	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) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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) (+ (* (* (* 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))) (sin kx) (/ kx (sin ky)) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))) (/ (sin th) (pow (sin kx) 3)))
9.0ms	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) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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) (+ (* (* (* 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))) (sin kx) (/ kx (sin ky)) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))) (/ (sin th) (pow (sin kx) 3)))
8.0ms	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) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (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) (+ (* (* (* 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))) (sin kx) (/ kx (sin ky)) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (* (+ (* (* ky ky) -1/6) 1) (/ (sin th) (sin kx))) (/ (sin th) (pow (sin kx) 3)))

simplify256.0ms (2.1%)

Memory

18.3MiB live, 251.4MiB allocated

Algorithm

1×	egg-herbie

Rules

8 622×	`lower-fma.f64`
8 622×	`lower-fma.f32`
6 694×	`lower-+.f64`
6 694×	`lower-+.f32`
6 674×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	948	13964
1	3143	13509
0	8122	12790

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 585

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))))))))))))
(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 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))))
(* -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))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (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 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 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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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 (+ (* 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)))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 kx))))
(* 1/2 (- 1 (cos (* 2 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)))
(+ (* -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 kx)
(sin kx)
(sin kx)
(sin kx)
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(- 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) (+ 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 th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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 (+ (* 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))))))))
(+ (* 1/2 (- 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)))))
(+ (* -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 kx)
(sin kx)
(sin kx)
(sin kx)
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(- 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) (+ 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 th) (pow (sin kx) 3))
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(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (* 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 (+ (* -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 (+ 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)))))
(/ 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))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 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 (/ (* (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) (+ 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 th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 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 (/ (* (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) (+ 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 th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 3))
(/ (sin th) (pow (sin kx) 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))))))
(/ (* 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))))
(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) (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)))))
(/ (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))
(/ kx ky)
(/ (+ kx (* 1/6 (* kx (pow ky 2)))) ky)
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/36 kx) (* 1/120 kx)))) (* -1/6 kx)))) ky)
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/5040 kx) (+ (* 1/720 kx) (* 1/6 (+ (* -1/36 kx) (* 1/120 kx))))))) (+ (* -1/36 kx) (* 1/120 kx)))) (* -1/6 kx)))) ky)
(* 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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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 (+ (* 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)))))
(* (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))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin 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))))))
(* -1/6 (/ (* (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)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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 (+ (* 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)))))
(* (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))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin ky))
(/ kx (sin 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))))))
(* -1/6 (/ (* (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 #s(literal 1/2 binary64) (sin.f64 ky)) (*.f64 kx kx) (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 (-.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)))) (.f64 kx kx)) (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))
(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))))))
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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
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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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(* (* 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)))))))))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))))) (.f64 th th) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))) (sin.f64 ky))) 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1/120 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/5040 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1/120 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1/120 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/5040 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1/120 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (+ 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1/120 binary64)) (sin.f64 kx))) (.f64 th th) (/.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #s(literal -1/6 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 (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))))
(fma.f64 (/.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) th (/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
(* 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))))
(fma.f64 (.f64 (fma.f64 (/.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)) th (/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))
(* 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))))
(fma.f64 (.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)) th (/.f64 th (pow.f64 (sin.f64 kx) #s(literal 3 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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(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
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(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
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(* ky (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (* (sin th) (+ 1 (* -1/6 (pow ky 2)))) (sin kx))))
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(/ (* (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) (+ 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))
(/ (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)))
(/ (* 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))))
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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))
(/.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))))
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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))))
(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 #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))))
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(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 (/.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 (-.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)))) (.f64 ky 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))
(/ (* 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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(/ (* 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 (sin.f64 th) #s(literal 1/12 binary64)) (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))))
(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)))
(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 (/.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 (-.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)))) (.f64 ky 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))
(* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))
(.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))))
(* 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 #s(literal 2 binary64) kx))) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/6 binary64) (.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 #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))))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)))) 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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(* 1/2 (- 1 (cos (* 2 kx))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64))
(+ (* 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))
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(* (* (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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (*.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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (*.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 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(+ (* 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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(+ (* 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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(+ (* 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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))
(* (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)))
(/ kx (sin ky))
(/.f64 kx (sin.f64 ky))
(/ kx (sin ky))
(/.f64 kx (sin.f64 ky))
(/ kx (sin ky))
(/.f64 kx (sin.f64 ky))
(/ kx (sin ky))
(/.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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))
(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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))
(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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))
(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 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))))
(* -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))

rewrite112.0ms (0.9%)

Memory

-46.4MiB live, 109.7MiB allocated

Rules

1 152×	`lower-*.f32`
1 136×	`lower-*.f64`
1 106×	`lower-fma.f32`
1 098×	`lower-fma.f64`
898×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	327
0	91	299
1	333	299
0	2581	299

Stop Event

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

Counts

23 → 302

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

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

eval237.0ms (2%)

Memory: 16.8MiB live, 237.8MiB allocated
Compiler: Compiled 30 535 to 2 168 computations (92.9% saved)

prune241.0ms (2%)

Memory

1.8MiB live, 243.6MiB allocated

Pruning

49 alts after pruning (47 fresh and 2 done)

	Pruned	Kept	Total
New	1 022	30	1 052
Fresh	7	17	24
Picked	3	2	5
Done	0	0	0
Total	1 032	49	1 081

Accuracy

100.0%

Counts

1 081 → 49

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.1%	(/.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	79.2%	(/.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)))))
	15.1%	(/.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))))
	78.9%	(/.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 (-.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)))))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))) (sin.f64 ky)))
	34.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky))) #s(literal 1/2 binary64) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) (sin.f64 ky)))
	41.1%	(/.f64 (sin.f64 th) (/.f64 (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 ky)))
	38.0%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	35.4%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	37.9%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
▶	33.2%	(/.f64 (sin.f64 th) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.7%	(/.f64 (sin.f64 th) (/.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 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.6%	(/.f64 (sin.f64 th) (/.f64 #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 ky)))
	33.0%	(/.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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
	41.7%	(/.f64 #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 (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)))
▶	41.8%	(/.f64 #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 (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)))
	41.7%	(/.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)))
	79.2%	(.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
	79.1%	(.f64 (/.f64 (sin.f64 th) (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))) (/.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))))
	79.3%	(.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))
	15.2%	(.f64 (/.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)))) (sin.f64 ky))
	79.1%	(.f64 (/.f64 (sin.f64 ky) (pow.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)) #s(literal 2 binary64))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	55.4%	(.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)))
	53.6%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th))
	48.6%	(.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))
	79.3%	(.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))
	86.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th))
▶	43.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	15.2%	(.f64 (/.f64 (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)))) (sin.f64 th))
	36.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) #s(approx (/ kx (sin ky)) (/.f64 kx ky)) (sin.f64 ky)))) (sin.f64 th))
	24.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	79.0%	(.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)))
	79.2%	(.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))
	54.5%	(.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))
	79.2%	(.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)))
	26.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin 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))) (sin.f64 th))
	21.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	17.7%	(.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))
▶	95.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (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.f64 th))
	41.8%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))))
	32.9%	#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 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
	26.3%	#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) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
	79.0%	#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 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
	20.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	21.6%	#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 (sin.f64 th) (sin.f64 kx))) ky))
	6.8%	#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))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	20.1%	#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)))
▶	20.2%	#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)))

Compiler

Compiled 2 370 to 1 547 computations (34.7% saved)

simplify69.0ms (0.6%)

Memory

9.7MiB live, 46.5MiB 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 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) 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 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	0	#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))
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 #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 (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	0	(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	384	(/.f64 (sin.f64 th) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
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	(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)))))
cost-diff	0	(*.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))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (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)))
cost-diff	0	(.f64 #s(approx (/ (sin ky) (sqrt (+ (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.f64 th))

Rules

1 824×	`lower-fma.f32`
1 814×	`lower-fma.f64`
836×	`lower-*.f32`
812×	`lower-*.f64`
464×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	658
0	126	650
1	180	650
2	261	642
3	446	621
4	816	621
5	1148	621
6	1537	621
7	1805	621
8	1888	621
9	1893	621
10	1893	621
0	1893	579

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize512.0ms (4.3%)

Memory

7.4MiB live, 520.7MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.171875	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.29916000976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	2.317092876196292	(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	33.41736383559537	#s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx))
accuracy	2.317092876196292	(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	15.10509972035183	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
accuracy	15.22228271148396	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 ky ky)))
accuracy	28.40610016922626	#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))
accuracy	0.170253759768442	(/.f64 (sin.f64 th) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
accuracy	2.317092876196292	(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	15.22228271148396	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
accuracy	34.21816427271731	#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	0.02734375	(.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)
accuracy	0.0703125	(fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64))
accuracy	28.49151913691686	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy	42.97460894060188	#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	0.2734375	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	0.29916000976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	0.33431625976844204	(*.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))
accuracy	2.5216530197617963	(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)))))

Samples

227.0ms	122×	2	valid
124.0ms	60×	1	valid
41.0ms	74×	0	valid

Compiler

Compiled 506 to 53 computations (89.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-mult: 78.0ms (27.9% of total)

ival-cos: 68.0ms (24.3% of total)

ival-sin: 32.0ms (11.5% of total)

adjust: 26.0ms (9.3% of total)

ival-pow2: 20.0ms (7.2% of total)

const: 14.0ms (5% of total)

ival-add: 14.0ms (5% of total)

ival-div: 11.0ms (3.9% of total)

ival-sqrt: 9.0ms (3.2% of total)

ival-sub: 7.0ms (2.5% of total)

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

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

exact: 0.0ms (0% of total)

series95.0ms (0.8%)

Memory

-5.8MiB live, 109.5MiB allocated

Counts

29 → 576

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	ky	@	-inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (/ (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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (+ (* (- 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))) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin kx) 2))
4.0ms	th	@	inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (/ (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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (+ (* (- 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))) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin kx) 2))
4.0ms	th	@	-inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (/ (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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (+ (* (- 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))) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin kx) 2))
4.0ms	ky	@	inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (/ (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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (+ (* (- 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))) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin kx) 2))
3.0ms	kx	@	-inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (/ (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 ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin ky) 2) (pow (sin kx) 2) (+ (* (- 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))) (- 1 (cos (+ ky ky))) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (pow (sin kx) 2))

simplify243.0ms (2%)

Memory

-7.5MiB live, 280.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 410×	`lower-fma.f64`
11 410×	`lower-fma.f32`
9 304×	`lower-*.f64`
9 304×	`lower-*.f32`
3 740×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	676	12982
1	2153	12249
2	7914	12231
0	8179	11789

Stop Event

1×	iter limit
1×	node limit

Counts

576 → 571

Calls

Call 1

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

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

rewrite88.0ms (0.7%)

Memory

8.9MiB live, 123.9MiB allocated

Rules

1 100×	`lower-fma.f32`
1 090×	`lower-fma.f64`
1 050×	`lower-*.f32`
1 028×	`lower-*.f64`
842×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	446
0	126	434
1	382	433
0	2430	399

Stop Event

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

Counts

29 → 286

Calls

Call 1

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

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

eval131.0ms (1.1%)

Memory: 20.2MiB live, 254.5MiB allocated
Compiler: Compiled 28 737 to 1 991 computations (93.1% saved)

prune240.0ms (2%)

Memory

-36.7MiB live, 363.4MiB allocated

Pruning

78 alts after pruning (74 fresh and 4 done)

	Pruned	Kept	Total
New	939	42	981
Fresh	10	32	42
Picked	3	2	5
Done	0	2	2
Total	952	78	1 030

Accuracy

100.0%

Counts

1 030 → 78

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.1%	(/.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	31.6%	(/.f64 (/.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(literal 1 binary64) (sin.f64 ky)))
	79.2%	(/.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)))))
	15.1%	(/.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))))
▶	31.5%	(/.f64 (.f64 (sin.f64 th) (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)))))
	38.0%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	35.4%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	37.9%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
	9.0%	(/.f64 (sin.f64 th) (/.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 #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 ky)))
	33.2%	(/.f64 (sin.f64 th) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.7%	(/.f64 (sin.f64 th) (/.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)))
	14.1%	(/.f64 (sin.f64 th) (/.f64 (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 ky)))
	31.6%	(/.f64 (sin.f64 th) (/.f64 #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 ky)))
	33.0%	(/.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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
	41.7%	(/.f64 #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 (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)))
	41.6%	(/.f64 #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 (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) (/.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)))))))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
✓	41.8%	(/.f64 #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 (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)))
	21.0%	(/.f64 #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 (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 (.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)) kx) kx)))) (sin.f64 ky)))
	26.2%	(/.f64 #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 (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 (.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)) kx) kx)))) (sin.f64 ky)))
	20.9%	(/.f64 #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 (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 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)))) (sin.f64 ky)))
	26.3%	(/.f64 #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 (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 ky)))
	20.4%	(/.f64 #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 (sqrt.f64 (fma.f64 #s(approx (- 1 (cos (+ ky ky))) (.f64 (.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)) 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)))
	21.9%	(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.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)))) (sin.f64 ky)))
	20.1%	(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) ky) ky)))) (sin.f64 ky)))
	21.8%	(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
	16.9%	(/.f64 #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 (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 ky)))
	16.9%	(/.f64 #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 #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 ky)))
	18.9%	(/.f64 #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 #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)))
	41.7%	(/.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)))
▶	18.9%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.5%	(/.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)))) (.f64 (sin.f64 th) (sin.f64 ky))))
	79.2%	(.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
	79.1%	(.f64 (/.f64 (sin.f64 th) (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))) (/.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))))
	79.3%	(.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))
	15.2%	(.f64 (/.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)))) (sin.f64 ky))
	31.7%	(.f64 (/.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))))) (sin.f64 ky))
	79.1%	(.f64 (/.f64 (sin.f64 ky) (pow.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)) #s(literal 2 binary64))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	55.4%	(.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)))
	53.6%	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th))
▶	48.6%	(.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))
	79.3%	(.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))
▶	86.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th))
	27.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	18.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	15.2%	(.f64 (/.f64 (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)))) (sin.f64 th))
	31.7%	(.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))
	36.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) #s(approx (/ kx (sin ky)) (/.f64 kx ky)) (sin.f64 ky)))) (sin.f64 th))
	24.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	79.2%	(.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))
	31.7%	(.f64 (neg.f64 (sin.f64 th)) (/.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)))) (neg.f64 (sin.f64 ky)))))
	79.2%	(.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)))
	26.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin 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))) (sin.f64 th))
	21.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	44.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (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)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 ky))) (sin.f64 th))
	32.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
	24.9%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th))
	41.6%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th))
	41.8%	#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))))
	79.0%	#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 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))))) (.f64 (sin.f64 ky) (sin.f64 th))))
	32.9%	#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 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
	26.3%	#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) kx))))) (.f64 (.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sin.f64 th))))
	26.3%	#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) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
	20.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	21.6%	#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 (sin.f64 th) (sin.f64 kx))) ky))
	6.8%	#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))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
✓	20.2%	#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)))
	20.2%	#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)))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)))) th)))
	9.4%	#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 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
	8.0%	#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) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
▶	20.4%	#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)))
	9.0%	#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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th th)))))
	8.0%	#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)))))
	7.3%	#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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.f64 (.f64 th th) th)))))

Compiler

Compiled 3 991 to 2 470 computations (38.1% saved)

simplify138.0ms (1.2%)

Memory

16.0MiB live, 170.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(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))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.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)))
cost-diff	0	(.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))
cost-diff	0	(sin.f64 th)
cost-diff	0	(*.f64 (sin.f64 th) (sin.f64 ky))
cost-diff	0	(/.f64 (.f64 (sin.f64 th) (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)))))
cost-diff	128	(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
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	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	384	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
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	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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)))))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th))
cost-diff	64	(+.f64 (pow.f64 (sin.f64 kx) #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)))))
cost-diff	128	(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))

Rules

5 580×	`lower-fma.f32`
5 576×	`lower-fma.f64`
3 080×	`lower-*.f32`
3 056×	`lower-*.f64`
2 350×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	638
0	123	624
1	181	624
2	281	617
3	564	602
4	1426	602
5	2778	602
6	4701	597
7	5967	597
8	7660	597
0	8132	563

Stop Event

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

Calls

Call 1

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

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

localize613.0ms (5.1%)

Memory

-12.0MiB live, 841.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0625	(fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64))
accuracy	0.16796875	(.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))
accuracy	0.171875	(/.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)))
accuracy	33.67760940562251	#s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky))
accuracy	2.317092876196292	(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))))
accuracy	2.911535219162689	(/.f64 (.f64 (sin.f64 th) (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)))))
accuracy	15.10509972035183	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
accuracy	36.45863532034979	#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)))
accuracy	2.317092876196292	(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	15.22228271148396	(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))
accuracy	28.49151913691686	#s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th))
accuracy	34.21816427271731	#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	0.02734375	(.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th)
accuracy	28.49151913691686	#s(approx (sin th) (.f64 #s(approx (+ ( (* th th) -1/6) 1) #s(literal 1 binary64)) th))
accuracy	29.026665812936788	#s(approx (+ (* (* th th) -1/6) 1) #s(literal 1 binary64))
accuracy	42.97460894060188	#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	0.28353500976844204	(pow.f64 (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
accuracy	0.3355725099495738	(+.f64 #s(literal 1/2 binary64) (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)))
accuracy	2.317092876196292	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))
accuracy	15.36576910540783	(-.f64 #s(literal 1/4 binary64) (pow.f64 (*.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)))

Samples

346.0ms	122×	2	valid
86.0ms	60×	1	valid
45.0ms	74×	0	valid

Compiler

Compiled 521 to 57 computations (89.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 422.0ms

ival-cos: 158.0ms (37.4% of total)

ival-mult: 66.0ms (15.6% of total)

adjust: 59.0ms (14% of total)

ival-sqrt: 34.0ms (8.1% of total)

ival-sin: 30.0ms (7.1% of total)

ival-div: 22.0ms (5.2% of total)

ival-add: 16.0ms (3.8% of total)

ival-pow2: 13.0ms (3.1% of total)

ival-sub: 10.0ms (2.4% of total)

const: 6.0ms (1.4% of total)

ival-hypot: 6.0ms (1.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series123.0ms (1%)

Memory

32.7MiB live, 262.1MiB allocated

Counts

31 → 612

Calls

Call 1

Inputs
#s(alt (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))) (patch (+.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (+.f64 (pow.f64 (sin.f64 kx) #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))))) (patch (+.f64 (pow.f64 (sin.f64 kx) #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))))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th)) #<representation binary64>) () ())
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#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>) () ())
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#s(alt (.f64 ky #s(literal 2 binary64)) (patch (.f64 ky #s(literal 2 binary64)) #<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 (-.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 th) (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))))) (patch (/.f64 (.f64 (sin.f64 th) (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))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 th) (sin.f64 ky)) (patch (.f64 (sin.f64 th) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (.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)) (patch (.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)) #<representation binary64>) () ())
#s(alt (/.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))) (patch (/.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))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt (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)) (patch (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)) #<representation binary64>) () ())
#s(alt (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (patch (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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)))))) (patch (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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)))))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (cos.f64 (+.f64 ky ky)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) #<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 #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))) (patch #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))) #<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 (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)))) (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 kx kx))) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) (patch #s(approx (sin ky) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) ky)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) (patch (fma.f64 #s(literal -1/6 binary64) (.f64 ky ky) #s(literal 1 binary64)) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
26.0ms	ky	@	inf	((+ 1/2 (* (cos (+ ky ky)) 1/2)) (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (* (- 1 (cos (+ kx kx))) 1/2) (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (sin th) (sin ky)) (sin th) (* (/ (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)))) (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2))))) (pow (* (cos (+ ky ky)) 1/2) 2) (+ (* (- 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))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky) (+ (* -1/6 (* ky ky)) 1))
14.0ms	ky	@	-inf	((+ 1/2 (* (cos (+ ky ky)) 1/2)) (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (* (- 1 (cos (+ kx kx))) 1/2) (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (sin th) (sin ky)) (sin th) (* (/ (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)))) (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2))))) (pow (* (cos (+ ky ky)) 1/2) 2) (+ (* (- 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))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky) (+ (* -1/6 (* ky ky)) 1))
10.0ms	kx	@	0	((+ 1/2 (* (cos (+ ky ky)) 1/2)) (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (* (- 1 (cos (+ kx kx))) 1/2) (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (sin th) (sin ky)) (sin th) (* (/ (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)))) (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2))))) (pow (* (cos (+ ky ky)) 1/2) 2) (+ (* (- 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))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky) (+ (* -1/6 (* ky ky)) 1))
9.0ms	kx	@	-inf	((+ 1/2 (* (cos (+ ky ky)) 1/2)) (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (* (- 1 (cos (+ kx kx))) 1/2) (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (sin th) (sin ky)) (sin th) (* (/ (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)))) (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2))))) (pow (* (cos (+ ky ky)) 1/2) 2) (+ (* (- 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))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky) (+ (* -1/6 (* ky ky)) 1))
8.0ms	kx	@	inf	((+ 1/2 (* (cos (+ ky ky)) 1/2)) (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2)))))) (* (/ (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 th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (* (- 1 (cos (* ky 2))) 1/2) (* ky 2) (sin th) (* (- 1 (cos (+ kx kx))) 1/2) (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (* (sin th) (sin ky)) (sin th) (* (/ (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)))) (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (sqrt (+ (pow (sin kx) 2) (/ (- 1/4 (pow (* (cos (+ ky ky)) 1/2) 2)) (+ 1/2 (* (cos (+ ky ky)) 1/2))))) (pow (* (cos (+ ky ky)) 1/2) 2) (+ (* (- 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))) (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (- 1 (cos (+ kx kx))) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky) (+ (* -1/6 (* ky ky)) 1))

simplify546.0ms (4.6%)

Memory

-143.0MiB live, 404.6MiB allocated

Algorithm

1×	egg-herbie

Rules

7 366×	`lower-fma.f64`
7 366×	`lower-fma.f32`
7 016×	`lower-*.f64`
7 016×	`lower-*.f32`
5 572×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	878	16395
1	2795	15457
2	6669	15113
0	8987	14410

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 606

Calls

Call 1

Inputs
(- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow kx 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3)))) (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))) (+ (* 2/45 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (+ (* 2/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))) (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 4)))))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* 1/2 (* (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3)))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))))
(* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))
(+ (* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3)))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(+ (* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3)))) (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))) (+ (* 2/45 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (+ (* 2/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))) (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 4))))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* 1/2 (* (* (sin ky) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 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)))))))))))
(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))))))))))))
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))))))
(sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))))
(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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)))))
(* (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))))))))))))
(* 1/2 (- 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 (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))))))))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 (+ (* 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))))
(* 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) (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)))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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)))))
(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 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))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 (+ (* 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))))))))
(* 1/2 (- 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) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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)))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 (* 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))))))
(sqrt (+ (* 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 (* 2 ky)))))
(- 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))))))
(* (* th (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 (+ (* 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))))
(* 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))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 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 (+ (* 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 (+ (* 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))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 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 (+ (* 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 (+ (* 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))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(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)))))
1
(+ 1 (* -1 (pow ky 2)))
(+ 1 (* (pow ky 2) (- (* 1/3 (pow ky 2)) 1)))
(+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/3 (* -2/45 (pow ky 2)))) 1)))
(pow (sin kx) 2)
(+ (pow ky 2) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) (pow (sin kx) 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* (* ky (* (sin th) (sqrt 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))))))))))))))))))))
(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 (sin th))
(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
(/ (* 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))))))
(pow ky 2)
(* (pow ky 2) (+ 1 (* -4/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 32/45 (pow ky 2)) 4/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 32/45 (* -64/315 (pow ky 2)))) 4/3))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
1/4
(+ 1/4 (* -1 (pow ky 2)))
(+ 1/4 (* (pow ky 2) (- (* 4/3 (pow ky 2)) 1)))
(+ 1/4 (* (pow ky 2) (- (* (pow ky 2) (+ 4/3 (* -32/45 (pow ky 2)))) 1)))
(* 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))))))))))))
(* 1/2 (- 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)))))
(* (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))))))))))))
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))))
1
(+ 1 (* -1/6 (pow ky 2)))
(+ 1 (* -1/6 (pow ky 2)))
(+ 1 (* -1/6 (pow ky 2)))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 (+ (* 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 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) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(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)))
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(- 1/4 (* 1/4 (pow (cos (* 2 ky)) 2)))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
(* 1/4 (pow (cos (* 2 ky)) 2))
(* 1/4 (pow (cos (* 2 ky)) 2))
(* 1/4 (pow (cos (* 2 ky)) 2))
(* 1/4 (pow (cos (* 2 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 (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)))))
(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 ky)
(sin ky)
(sin ky)
(* -1/6 (pow ky 2))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -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 (+ (* 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 (* 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) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (sin ky) (sin th))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(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)))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(* 1/4 (pow (cos (neg (* -2 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)))))
(- 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))))))
(+ (* 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)))))
(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))))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(* -1/6 (pow ky 2))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))

Outputs
(- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow kx 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (fma.f64 kx kx (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (fma.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (.f64 kx kx) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
(fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (fma.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) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(+ (* -1/2 (* (* (pow kx 2) (* (sin ky) (sin th))) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (.f64 kx kx))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))) (.f64 (sin.f64 th) (sin.f64 ky))))
(+ (* (* (sin ky) (sin th)) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (* (sin ky) (sin th)) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sin.f64 ky) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 2 binary64)))) (sin.f64 th)))) (sqrt.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sin.f64 th) (sin.f64 ky))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) #s(literal 3 binary64)))))) (.f64 kx kx) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))) (.f64 (sin.f64 th) (sin.f64 ky))))
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(* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(+ (* -1/2 (* (* (pow kx 2) (sin ky)) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))
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(+ (* (sin ky) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (sin ky) (sqrt (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3))))) (* 1/2 (* (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 2))) (* 3/4 (/ 1 (pow (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))) 3)))))) (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
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(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
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(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
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(* (* (sin ky) (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 ky))))))
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(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
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1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
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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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(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) (*.f64 kx kx) (sin.f64 ky))
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(sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))
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(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* 1/2 (* (pow kx 2) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))))
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(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* (pow kx 2) (+ (* -1/2 (* (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))
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(+ (sqrt (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))) (* (pow kx 2) (+ (* 1/2 (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow kx 2) (+ (* -1/2 (* (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/2 (* (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (sqrt (/ 1 (- (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))))))))
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(* 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)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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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(sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (* 1/2 (- 1 (cos (* 2 ky))))))
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(* (* th (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))))
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(* th (+ (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))))))))))))
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(* (* 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)))))))
(.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))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 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)))))) (* 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))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 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))))) (* (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))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64)))) (.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 (+ (* 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)))))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 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))))))))) (* 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)))))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 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 (+ (* 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)))))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64)))) (.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
(* 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 (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)))))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 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))))))))) (* 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)))))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 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 (+ (* 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)))))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64)))) (.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))
(*.f64 th (sin.f64 ky))
(* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))
(.f64 (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))
(.f64 (fma.f64 (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 binary64))) (.f64 th th) (sin.f64 ky)) th)
(* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))
(.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64))) (.f64 th th) (.f64 #s(literal -1/6 binary64) (sin.f64 ky))) (.f64 th th) (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 (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))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 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)))))) (* 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))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal 1/120 binary64) (.f64 th th) #s(literal -1/6 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))))) (* (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))))) (.f64 (sin.f64 ky) (fma.f64 #s(literal -1/5040 binary64) (.f64 th th) #s(literal 1/120 binary64)))) (.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)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))) (*.f64 (sin.f64 th) (sin.f64 ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 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 th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(sin th)
(sin.f64 th)
(* -1/6 (pow th 3))
(.f64 (.f64 (*.f64 th th) th) #s(literal -1/6 binary64))
(* (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))
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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))
(/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.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 #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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.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 (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))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (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 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 kx)) (.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)))) (sin.f64 th)) (fma.f64 (.f64 #s(literal -1/12 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) (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)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(* (* ky (* (sin th) (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 (.f64 (sin.f64 th) ky) (sqrt.f64 #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 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 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 (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)) (sin.f64 th)))) 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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(pow ky 2)
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(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
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(* (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 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* (* 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))
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(* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))
(.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 th)) ky)
(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))
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(* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))
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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))
(/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (.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))))
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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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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 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -4/3 (pow ky 2))))
(.f64 (fma.f64 #s(literal -4/3 binary64) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 32/45 (pow ky 2)) 4/3))))
(.f64 (fma.f64 (fma.f64 #s(literal 32/45 binary64) (.f64 ky ky) #s(literal -4/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 32/45 (* -64/315 (pow ky 2)))) 4/3))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -64/315 binary64) (.f64 ky ky) #s(literal 32/45 binary64)) (.f64 ky ky) #s(literal -4/3 binary64)) (.f64 ky ky) #s(literal 1 binary64)) (*.f64 ky 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 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (.f64 ky ky) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) (.f64 ky ky) (sin.f64 kx))
1/4
#s(literal 1/4 binary64)
(+ 1/4 (* -1 (pow ky 2)))
(-.f64 #s(literal 1/4 binary64) (*.f64 ky ky))
(+ 1/4 (* (pow ky 2) (- (* 4/3 (pow ky 2)) 1)))
(fma.f64 (fma.f64 (.f64 ky ky) #s(literal 4/3 binary64) #s(literal -1 binary64)) (.f64 ky ky) #s(literal 1/4 binary64))
(+ 1/4 (* (pow ky 2) (- (* (pow ky 2) (+ 4/3 (* -32/45 (pow ky 2)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -32/45 binary64) (.f64 ky ky) #s(literal 4/3 binary64)) (.f64 ky ky) #s(literal -1 binary64)) (*.f64 ky ky) #s(literal 1/4 binary64))
(* 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)))
(* 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 (+.f64 (/.f64 #s(literal -1/4 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 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))))
(* 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)))
(* (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))))))))))
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(+ (* (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))))))))))))
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ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
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(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
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(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
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1
#s(literal 1 binary64)
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(+ 1 (* -1/6 (pow ky 2)))
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(+ 1 (* -1/6 (pow ky 2)))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
(fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* 1/2 (cos (* 2 ky))))
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(+ 1/2 (* 1/2 (cos (* 2 ky))))
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(+ 1/2 (* 1/2 (cos (* 2 ky))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky)))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (cos (* 2 ky))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (* 2 ky)))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (* 2 ky)) 2) (+ 1/2 (* 1/2 (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 th) (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)))))
(.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)))))
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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 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))))
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(* 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))))
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(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* (* (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))
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(* (sin ky) (sin th))
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(* (sin ky) (sin th))
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(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (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) (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)))))
(*.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)))))
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin ky)
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(sin ky)
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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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(sin ky)
(sin.f64 ky)
(sin ky)
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(* -1/6 (pow ky 2))
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(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
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(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
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(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
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(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
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(+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
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(- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))))
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(* (sin ky) (sqrt (/ 1 (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -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 (+ (* 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)))
(* 1/2 (- 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))))
(.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))))
(.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))))
(.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.f64 ky #s(literal 2 binary64))
(* 2 ky)
(*.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)))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (sin ky) (sin th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(* (sin ky) (sin th))
(*.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) (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))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(- 1/4 (* 1/4 (pow (cos (neg (* -2 ky))) 2)))
(fma.f64 #s(literal -1/4 binary64) (pow.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(sqrt (- (+ (* 1/4 (/ 1 (+ 1/2 (* 1/2 (cos (neg (* -2 ky))))))) (pow (sin kx) 2)) (* 1/4 (/ (pow (cos (neg (* -2 ky))) 2) (+ 1/2 (* 1/2 (cos (neg (* -2 ky)))))))))
(sqrt.f64 (fma.f64 (/.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1 binary64))) #s(literal -1/2 binary64) (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(* 1/4 (pow (cos (neg (* -2 ky))) 2))
(.f64 (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(+ (* 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 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 #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)))))))
(+ (* 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 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 #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)))))))
(- 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 (+ (* 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))))))))
(+ (* 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 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 #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)))))))
(+ (* 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 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 #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))))))))
(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))))))))
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(sin ky)
(sin.f64 ky)
(* -1/6 (pow ky 2))
(.f64 (.f64 ky ky) #s(literal -1/6 binary64))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(* (pow ky 2) (- (/ 1 (pow ky 2)) 1/6))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))

rewrite120.0ms (1%)

Memory

-0.5MiB live, 223.2MiB allocated

Rules

1 374×	`lower-fma.f32`
1 370×	`lower-fma.f64`
1 140×	`lower-*.f32`
1 118×	`lower-*.f64`
946×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	495
0	123	483
1	416	351
0	3020	330

Stop Event

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

Counts

31 → 453

Calls

Call 1

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

Outputs
(*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))
(.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(*.f64 (cos.f64 ky) (cos.f64 ky))
(*.f64 (cos.f64 kx) (cos.f64 kx))
(.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))
(pow.f64 (cos.f64 ky) #s(literal 2 binary64))
(pow.f64 (cos.f64 kx) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64)) #s(literal 1/4 binary64)) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64))))
(/.f64 (+.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 #s(literal 0 binary64))) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 4 binary64))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 6 binary64))) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (fma.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) #s(literal 1/16 binary64))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64) (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/4 binary64) (cos.f64 (+.f64 kx kx))))))
(/.f64 (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64)) (fma.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(/.f64 (neg.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64))))
(/.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))))
(+.f64 (*.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #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 1 binary64) (-.f64 (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 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 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 (sin.f64 ky) #s(literal 4 binary64)))))
(*.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (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 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 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 (sin.f64 ky) #s(literal 4 binary64)))))
(/.f64 (fma.f64 (neg.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64) (.f64 (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))))) (.f64 (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))))) (.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (fma.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64) (.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))))) (.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
(/.f64 (fma.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))) (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64))))) (.f64 #s(literal 2 binary64) (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (-.f64 (cos.f64 #s(literal 0 binary64)) (cos.f64 (+.f64 kx kx))) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)))) (.f64 #s(literal 2 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #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 1/2 binary64) (-.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))))
(/.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 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 (sin.f64 ky) #s(literal 4 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 (sin.f64 ky) #s(literal 4 binary64))) (+.f64 (pow.f64 (sin.f64 ky) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))))
(fma.f64 (/.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) #s(literal 1/8 binary64) #s(literal 1/8 binary64))) (fma.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) (-.f64 (.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 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)))
(fma.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 ky))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 kx))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (neg.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #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 #s(literal 0 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)))
(fma.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)))
(fma.f64 #s(literal 1 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)))
(fma.f64 (sin.f64 ky) (sin.f64 ky) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 kx kx))))) #s(literal -1/4 binary64) #s(literal 1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 kx) (sin.f64 kx) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(-.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64) (/.f64 #s(literal 1/4 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64)))) (.f64 (/.f64 (+.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) (cos.f64 (+.f64 kx kx)))) #s(literal 1/2 binary64)))
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(.f64 (-.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 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(*.f64 (-.f64 #s(literal 1 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 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) (neg.f64 (cos.f64 (+.f64 kx kx))))) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (neg.f64 (cos.f64 (+.f64 kx kx))) (neg.f64 (cos.f64 (+.f64 kx kx)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 kx kx)))))))
(/.f64 (neg.f64 (-.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))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))))
(/.f64 (-.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) (cos.f64 (+.f64 kx kx))))
(/.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 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) (-.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 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #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 #s(literal 1 binary64) (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 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 (+.f64 kx kx)) #s(literal 3 binary64)) (fma.f64 (cos.f64 (+.f64 kx kx)) (+.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx)))
(+.f64 (-.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))) #s(literal 1/2 binary64)))
(+.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 #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))) #s(literal 1/4 binary64)) (pow.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))) #s(literal 1/4 binary64)))
(pow.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))) #s(literal 1/2 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 kx kx))) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.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)))) #s(literal 1/2 binary64)))
#s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) ky))
(.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64))))))
(/.f64 (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64)) (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64)))
(/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))))
(/.f64 (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64)) (fma.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky)) #s(literal -1 binary64))))
(/.f64 #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 (.f64 ky ky) #s(literal -1/6 binary64)))) (fma.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (.f64 (*.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(fma.f64 (.f64 #s(literal -1/6 binary64) ky) (.f64 ky #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (*.f64 #s(literal -1/6 binary64) ky) ky #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 ky ky) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/6 binary64) (*.f64 ky ky) #s(literal 1 binary64))
(fma.f64 ky (*.f64 #s(literal -1/6 binary64) ky) #s(literal 1 binary64))
(-.f64 (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 ky ky) (.f64 ky ky))) (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal -1 binary64))))
(+.f64 (.f64 (.f64 ky ky) #s(literal -1/6 binary64)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 ky ky) #s(literal -1/6 binary64)))

eval166.0ms (1.4%)

Memory: 5.4MiB live, 308.6MiB allocated
Compiler: Compiled 35 457 to 2 686 computations (92.4% saved)

prune320.0ms (2.7%)

Memory

4.2MiB live, 534.0MiB allocated

Pruning

88 alts after pruning (82 fresh and 6 done)

	Pruned	Kept	Total
New	1 086	42	1 128
Fresh	29	40	69
Picked	3	2	5
Done	0	4	4
Total	1 118	88	1 206

Accuracy

100.0%

Counts

1 206 → 88

Alt Table

Click to see full alt table

Status	Accuracy	Program
	79.1%	(/.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))
	16.9%	(/.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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(literal 1 binary64) (sin.f64 ky)))
	6.2%	(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky))) (.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)))) #s(literal 2 binary64)))
	79.2%	(/.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)))))
	15.1%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 kx kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64))))
	33.7%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
	36.3%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
	33.7%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
	36.2%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))
	42.6%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
✓	31.5%	(/.f64 (.f64 (sin.f64 th) (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)))))
	33.0%	(/.f64 (.f64 (sin.f64 th) (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)))))
	14.8%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
	31.5%	(/.f64 (.f64 (sin.f64 th) (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)))))
	32.9%	(/.f64 (.f64 (sin.f64 th) (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))))))))
	25.9%	(/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)))))
	9.0%	(/.f64 (sin.f64 th) (/.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 #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 ky)))
	33.2%	(/.f64 (sin.f64 th) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	31.7%	(/.f64 (sin.f64 th) (/.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)))
	14.1%	(/.f64 (sin.f64 th) (/.f64 (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 ky)))
	31.6%	(/.f64 (sin.f64 th) (/.f64 #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 ky)))
	33.0%	(/.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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
	26.3%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) 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)))))
	17.1%	(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))
	41.7%	(/.f64 #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 (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)))
✓	41.8%	(/.f64 #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 (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)))
	21.0%	(/.f64 #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 (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 (.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)) kx) kx)))) (sin.f64 ky)))
	20.4%	(/.f64 #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 (sqrt.f64 (fma.f64 #s(approx (- 1 (cos (+ ky ky))) (.f64 (.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)) 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)))
	41.7%	(/.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)))
	26.3%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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.f64 ky)))
	21.0%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	26.5%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))) (sin.f64 ky)))
	22.0%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	20.1%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
	21.9%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
	25.7%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 ky)))
	16.9%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) (sin.f64 ky)))
	7.0%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 #s(literal 1 binary64) (/.f64 (fma.f64 ky ky #s(literal 0 binary64)) (.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	18.9%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
	9.8%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 ky)))
	16.8%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #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)))
	18.8%	(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
	31.5%	(/.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)))) (.f64 (sin.f64 th) (sin.f64 ky))))
	16.7%	(/.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)))) (.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
	79.2%	(.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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
	79.1%	(.f64 (/.f64 (sin.f64 th) (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))) (/.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))))
	79.3%	(.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))
	15.2%	(.f64 (/.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)))) (sin.f64 ky))
	31.7%	(.f64 (/.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))))) (sin.f64 ky))
	79.1%	(.f64 (/.f64 (sin.f64 ky) (pow.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)) #s(literal 2 binary64))) (sin.f64 th))
✓	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	55.4%	(.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)))
	46.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	18.7%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	15.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 kx kx)) (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 kx kx))))) #s(literal 1/2 binary64)))) (sin.f64 th))
	31.7%	(.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))
	16.9%	(.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))))) #s(approx (sin th) (.f64 (fma.f64 (*.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)))
	36.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) #s(approx (/ kx (sin ky)) (/.f64 kx ky)) (sin.f64 ky)))) (sin.f64 th))
	24.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	16.9%	(.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) (sin.f64 ky))
	46.7%	(.f64 (/.f64 #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)) (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))
	50.7%	(.f64 (/.f64 #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
	31.5%	(.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))))) (.f64 (sin.f64 th) (sin.f64 ky)))
	31.7%	(.f64 (sin.f64 ky) (.f64 (sin.f64 th) (/.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)))))))
	21.5%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	44.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (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)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 ky))) (sin.f64 th))
	32.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (sin.f64 th))
	24.9%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th))
	41.6%	#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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)))))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
	41.8%	#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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))))))))))
	79.0%	#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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))))
	32.9%	#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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))))
	26.3%	#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) kx))))) (.f64 (.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sin.f64 th))))
	20.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx)))
	21.6%	#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 (sin.f64 th) (sin.f64 kx))) ky))
	6.8%	#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))
✓	32.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))))))
✓	20.2%	#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)))
	20.2%	#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)))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (*.f64 th th))))) th)))
	19.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)))) th)))
	9.4%	#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 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) th)))
	8.0%	#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) (.f64 (.f64 th th) #s(literal -1/6 binary64))) th)))
✓	20.4%	#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)))
	7.3%	#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)))))
	9.0%	#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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th th)))))
	8.0%	#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)))))

Compiler

Compiled 5 498 to 1 899 computations (65.5% saved)

regimes405.0ms (3.4%)

Memory

2.2MiB live, 535.2MiB allocated

Counts

144 → 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)))))
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#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 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))) (*.f64 (sin.f64 ky) (sin.f64 th))))
(/.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)))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))))) (fma.f64 #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 ky) th) th) (sin.f64 ky))) 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))))) (/.f64 #s(literal 1 binary64) (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))))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 th))
(.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))
(/.f64 #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 (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) (/.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)))))))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
#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)))))))
(.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 (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 (-.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)))))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 kx kx)) #s(literal 1 binary64))))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.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 #s(approx (/ (sin ky) (sqrt (+ (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.f64 th))
(.f64 (/.f64 (sin.f64 ky) (pow.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)) #s(literal 2 binary64))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #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))))))) #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 (pow.f64 (sin.f64 kx) #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))))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (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))) (/.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))))

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

Calls

9 calls:

67.0ms	(sin.f64 th)
47.0ms	th
46.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
41.0ms	(*.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))
41.0ms	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)

regimes363.0ms (3%)

Memory

14.5MiB live, 665.2MiB allocated

Counts

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

Calls

9 calls:

51.0ms	ky
45.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
41.0ms	(sin.f64 kx)
38.0ms	(sin.f64 ky)
38.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
99.4%	2	`kx`
93.0%	2	`th`
88.4%	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))`
99.6%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
99.3%	3	`(sin.f64 ky)`
99.3%	2	`ky`
99.4%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
99.4%	3	`(sin.f64 kx)`
93.0%	3	`(sin.f64 th)`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes101.0ms (0.8%)

Memory

-1.6MiB live, 116.7MiB allocated

Counts

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

Outputs

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

2 calls:

64.0ms	kx
30.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
99.4%	2	`kx`
99.4%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes337.0ms (2.8%)

Memory

1.1MiB live, 440.7MiB allocated

Counts

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

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

Calls

9 calls:

61.0ms	(sin.f64 kx)
40.0ms	ky
37.0ms	th
36.0ms	(*.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))
32.0ms	kx

Results

Accuracy	Segments	Branch
71.8%	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))`
77.9%	4	`(sin.f64 th)`
77.7%	3	`th`
86.1%	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)))))`
77.7%	3	`(sin.f64 ky)`
79.5%	4	`(sin.f64 kx)`
77.8%	2	`ky`
77.8%	2	`kx`
77.7%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes36.0ms (0.3%)

Memory

10.4MiB live, 56.5MiB 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 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 (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))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) 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)))))
(/.f64 (sin.f64 th) (/.f64 (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 ky)))
(.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) (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 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)))
(/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)))))
#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) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #s(literal 2 binary64)))))
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#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 ky #s(literal 2 binary64)))))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (sin.f64 th)) (sin.f64 ky))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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))))
(/.f64 (/.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(literal 1 binary64) (sin.f64 ky)))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))))))))))
(/.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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #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 ky)))
(.f64 (/.f64 #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)) (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 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
(/.f64 (sin.f64 th) (/.f64 (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 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) (*.f64 kx kx))))) (sin.f64 ky)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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)))))))) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))) th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) (pow.f64 (sin.f64 ky) #s(literal 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 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
(/.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 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
(/.f64 #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 (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 th) (/.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 #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 ky)))
(/.f64 #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 (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 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (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)))
(.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))

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

Calls

1 calls:

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)))))

Results

Accuracy	Segments	Branch
85.5%	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)

regimes34.0ms (0.3%)

Memory

-5.8MiB live, 69.5MiB allocated

Counts

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

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

Calls

1 calls:

27.0ms

(/.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
85.4%	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)

regimes38.0ms (0.3%)

Memory

-19.1MiB live, 60.5MiB allocated

Counts

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

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

Calls

1 calls:

27.0ms

(/.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
85.4%	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)

regimes30.0ms (0.2%)

Memory

25.8MiB live, 62.4MiB allocated

Counts

88 → 5

Calls

Call 1

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

Outputs
(/.f64 (.f64 (sin.f64 th) (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) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))))
(.f64 (/.f64 #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)))) (.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))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) #s(approx (/ kx (sin ky)) (/.f64 kx ky)) (sin.f64 ky)))) (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
85.3%	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

-18.5MiB live, 54.8MiB allocated

Counts

79 → 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 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 (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))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) 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)))))
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(/.f64 (.f64 (sin.f64 th) (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))))))))
(/.f64 (.f64 (sin.f64 th) (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)))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))))))

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

Calls

1 calls:

22.0ms

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

Results

Accuracy	Segments	Branch
85.3%	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)

regimes103.0ms (0.9%)

Memory

19.6MiB live, 176.4MiB allocated

Counts

78 → 2

Calls

Call 1

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

Outputs

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

Calls

4 calls:

31.0ms	(/.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)))))
23.0ms	kx
23.0ms	ky
21.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
71.1%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
71.1%	3	`kx`
77.6%	2	`ky`
76.7%	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 31 to 23 computations (25.8% saved)

regimes236.0ms (2%)

Memory

16.6MiB live, 366.9MiB 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 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 (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))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) 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)))))
(/.f64 (sin.f64 th) (/.f64 (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 ky)))
(.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) (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 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)))
(/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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)))))
#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) kx))))) (.f64 (.f64 ky (sin.f64 th)) (sqrt.f64 #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) kx))))) (.f64 (.f64 ky (sqrt.f64 #s(literal 2 binary64))) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (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 #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 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 (cos.f64 (+.f64 kx kx)) #s(literal 1/2 binary64))))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.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)))) (.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (sin.f64 ky))))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 kx kx)))) (sin.f64 ky)))
(/.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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(literal 1 binary64) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 ky #s(literal 2 binary64))))))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 #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)))
(/.f64 #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 (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 ky)))
(/.f64 #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 (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 ky)))
(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #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 #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)))
(/.f64 #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 #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 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
(/.f64 #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 (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 (.f64 (fma.f64 #s(literal -1/3 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx) kx)))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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))))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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.f64 ky)))
(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.f64 (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/3 binary64) #s(literal 1 binary64)) ky) ky)))) (sin.f64 ky)))
(/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 #s(literal 1 binary64) (/.f64 (fma.f64 ky ky #s(literal 0 binary64)) (.f64 (fma.f64 ky ky #s(literal 0 binary64)) (+.f64 kx kx)))))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 #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 (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 (.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)) kx) kx)))) (sin.f64 ky)))
(/.f64 #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 (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64) (.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)))) (sin.f64 ky)))
(/.f64 #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 (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 (.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)) kx) kx)))) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(/.f64 #s(approx (sin th) (.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 (sqrt.f64 (fma.f64 #s(approx (- 1 (cos (+ ky ky))) (.f64 (.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)) 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(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (.f64 #s(approx (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky))) (sin.f64 ky))) (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 #s(approx (/ (sin ky) (sqrt (+ (pow (sin 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))) (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 kx kx))) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.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))))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (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)))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 #s(literal 1/2 binary64) kx) #s(approx (/ kx (sin ky)) (/.f64 kx ky)) (sin.f64 ky)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 th) (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) (.f64 (sin.f64 th) (/.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)))))))
(.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))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.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)))
(/.f64 (sin.f64 th) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.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 #s(literal 2 binary64) kx))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.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 ky #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (sin.f64 ky)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 kx #s(literal 2 binary64)))) #s(literal 1/2 binary64) (.f64 ky ky)))))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky))) (.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)))) #s(literal 2 binary64)))
(/.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)))) (.f64 (sin.f64 th) (sin.f64 ky))))

Outputs

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

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

Calls

9 calls:

44.0ms	(/.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)))))
30.0ms	ky
28.0ms	th
22.0ms	(sin.f64 th)
22.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Results

Accuracy	Segments	Branch
63.9%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
64.0%	3	`kx`
53.3%	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))`
49.5%	5	`(sin.f64 th)`
69.8%	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)))))`
48.7%	4	`th`
65.0%	3	`(sin.f64 ky)`
64.1%	4	`(sin.f64 kx)`
64.7%	2	`ky`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes40.0ms (0.3%)

Memory

12.1MiB live, 88.0MiB allocated

Counts

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

Outputs

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

(*.f64 (/.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))))) (sin.f64 ky))

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

Calls

2 calls:

18.0ms	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)))))

Results

Accuracy	Segments	Branch
45.4%	2	`ky`
65.1%	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 20 to 14 computations (30% saved)

regimes21.0ms (0.2%)

Memory

7.7MiB live, 46.0MiB allocated

Counts

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

Outputs

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

(*.f64 (/.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))))) (sin.f64 ky))

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

Calls

1 calls:

17.0ms

(/.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
65.1%	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)

regimes34.0ms (0.3%)

Memory

-45.2MiB live, 22.2MiB allocated

Counts

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

Outputs

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

Calls

1 calls:

15.0ms

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

Results

Accuracy	Segments	Branch
65.1%	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)

regimes76.0ms (0.6%)

Memory

18.7MiB live, 95.5MiB allocated

Counts

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

Outputs

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

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

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

Calls

4 calls:

23.0ms	kx
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)))))
16.0ms	(sin.f64 ky)
15.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
57.7%	3	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
57.9%	3	`kx`
52.7%	3	`(sin.f64 ky)`
62.9%	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 32 to 24 computations (25% saved)

regimes63.0ms (0.5%)

Memory

-21.7MiB live, 56.5MiB allocated

Counts

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

Outputs

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

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

Calls

4 calls:

26.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
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)))))
9.0ms	(sin.f64 kx)
9.0ms	kx

Results

Accuracy	Segments	Branch
53.5%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
53.5%	2	`kx`
54.0%	3	`(sin.f64 kx)`
55.5%	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 32 to 24 computations (25% saved)

regimes9.0ms (0.1%)

Memory

22.1MiB live, 22.1MiB allocated

Counts

25 → 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 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 (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))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) 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)))))
(/.f64 (sin.f64 th) (/.f64 (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 ky)))
(.f64 (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) (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 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)))

Outputs

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

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

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

Calls

1 calls:

7.0ms

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

Results

Accuracy	Segments	Branch
56.9%	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)

regimes47.0ms (0.4%)

Memory

-18.9MiB live, 91.4MiB allocated

Counts

21 → 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 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 (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))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) #s(approx (* (- 1 (cos (+ kx kx))) 1/2) (*.f64 kx kx)))))
(/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))

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

6 calls:

9.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
9.0ms	(*.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))
8.0ms	(sin.f64 kx)
6.0ms	kx
6.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
41.8%	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))`
42.8%	2	`(sin.f64 ky)`
48.1%	3	`(sin.f64 kx)`
44.4%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
44.3%	2	`kx`
49.3%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 56 to 41 computations (26.8% saved)

regimes53.0ms (0.4%)

Memory

10.7MiB live, 94.9MiB allocated

Counts

16 → 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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 th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (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 ky)))

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

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

Calls

9 calls:

9.0ms	th
7.0ms	(sin.f64 ky)
5.0ms	(sin.f64 th)
5.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
5.0ms	ky

Results

Accuracy	Segments	Branch
36.9%	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))`
32.9%	1	`(sin.f64 ky)`
32.9%	1	`kx`
32.9%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
32.9%	1	`(sin.f64 th)`
32.9%	1	`ky`
32.9%	1	`th`
32.9%	1	`(sin.f64 kx)`
36.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes6.0ms (0%)

Memory

12.1MiB live, 12.1MiB 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.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)) (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

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
36.6%	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 16 to 11 computations (31.3% saved)

regimes44.0ms (0.4%)

Memory

7.6MiB live, 81.3MiB 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) (.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 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) th) (.f64 th 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 #s(approx (+ ( (* th th) -1/6) 1) (.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 th th)) #s(literal 1/6 binary64)) th) th)) 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 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (.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 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) th) (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.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 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 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)) #s(approx (sin th) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (.f64 th th)))) (fma.f64 (.f64 (.f64 (.f64 th th) (.f64 th th)) #s(literal 1/36 binary64)) (.f64 #s(literal -1/6 binary64) (.f64 th th)) #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) #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:

7.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
6.0ms	(sin.f64 kx)
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	th
4.0ms	(sin.f64 th)

Results

Accuracy	Segments	Branch
22.2%	2	`(sin.f64 ky)`
22.5%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
20.4%	1	`(sin.f64 th)`
20.4%	1	`(sin.f64 kx)`
20.4%	1	`th`
22.5%	2	`kx`
20.4%	1	`ky`
25.1%	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))`
24.3%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 69 to 51 computations (26.1% saved)

regimes16.0ms (0.1%)

Memory

-17.5MiB live, 21.5MiB 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

6 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)))))
2.0ms	(*.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	(sin.f64 ky)
1.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
1.0ms	kx

Results

Accuracy	Segments	Branch
20.4%	1	`th`
20.4%	1	`(sin.f64 ky)`
20.4%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
20.4%	1	`kx`
20.4%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
20.4%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`

Compiler

Compiled 55 to 40 computations (27.3% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.9255492701071587e-9	1.558875032310667e-6

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.9255492701071587e-9	1.558875032310667e-6

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	0.9802672025256338	0.9986622739655636
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9999996186923419	1.0
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

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	0.9999996186923419	1.0
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9999996186923419	1.0
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9999996186923419	1.0
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9999996186923419	1.0
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307
0.0ms	-0.9984169722449785	-0.967414111751596

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch18.0ms (0.2%)

Memory

-8.4MiB live, 28.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	88793784296.94249	184906962036.02048

Samples

12.0ms

80×

valid

Compiler

Compiled 267 to 178 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sin: 6.0ms (62.8% of total)

ival-pow2: 2.0ms (20.9% of total)

ival-div: 1.0ms (10.5% of total)

ival-sqrt: 1.0ms (10.5% of total)

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

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

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

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

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9986622739655636	0.9999996186923419
0.0ms	-0.7099175610838557	-0.7067062507572397

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9986622739655636	0.9999996186923419
0.0ms	-0.893137508197428	-0.8787810945758692

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7024484545263494	0.7123532103407894
0.0ms	-0.893137508197428	-0.8787810945758692

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.7024484545263494	0.7123532103407894
0.0ms	-0.893137508197428	-0.8787810945758692

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.03173598784099442	-0.0019193998314031354

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.030244990013449817	0.0714697617985605

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.030244990013449817	0.0714697617985605
0.0ms	-0.0019193998314031354	2.378873090475732e-307

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.283432308989543e-8	3.7767547411508225e-5

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	7.422379717579819e-72	3.4797256112295175e-68

Compiler

Compiled 22 to 19 computations (13.6% saved)

bsearch16.0ms (0.1%)

Memory

-13.1MiB live, 23.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	6.645394710704344e-68	1.195796241502381e-59

Samples

10.0ms

144×

valid

Compiler

Compiled 211 to 136 computations (35.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sin: 3.0ms (68.6% of total)

ival-mult: 1.0ms (22.9% 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	7.699355506864031e-297	8.274045128458784e-297

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify39.0ms (0.3%)

Memory

8.6MiB live, 45.1MiB allocated

Algorithm

1×	egg-herbie

Rules

142×	`unsub-neg_binary64`
108×	`*-commutative_binary64`
84×	`distribute-lft-neg-in_binary64`
78×	`distribute-neg-in_binary64`
72×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	269	2926
1	329	2926
2	363	2926
3	411	2926
4	517	2926
5	585	2926
6	652	2926
7	686	2926
8	718	2926
9	727	2926
10	728	2926

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
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(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 -7926335344172073/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 799388933858263/1125899906842624 binary64)) (.f64 (/.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))))) (sin.f64 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 -7926335344172073/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 799388933858263/1125899906842624 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)) #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 -5764607523034235/288230376151711744 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #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 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #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 -1152921504606847/1152921504606846976 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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))))) (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 3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) 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))))) #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 3022314549036573/151115727451828646838272 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 2486616182048933/248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 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 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (.f64 kx kx) kx)) #s(literal -1/2 binary64))) 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 2894802230932905/28948022309329048855892746252171976963317496166410141009864396001978282409984 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 5890680864316837/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736 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 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 3022314549036573/604462909807314587353088 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (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)))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 3022314549036573/604462909807314587353088 binary64)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) 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 -2206763817411543/2251799813685248 binary64)) (/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 #s(approx (+ ( (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (pow.f64 (sin.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 -1152921504606847/1152921504606846976 binary64)) #s(approx (/ (sin th) (/ (sqrt (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2))) (sin ky))) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx))))))))) (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 3602879701896397/72057594037927936 binary64)) (.f64 (/.f64 #s(approx (sin ky) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 ky ky) #s(literal 1 binary64)) ky)) (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 4458563631096791/4503599627370496 binary64)) (/.f64 #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 (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) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 th))))))
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(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -7926335344172073/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 799388933858263/1125899906842624 binary64)) (.f64 (/.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))))) (sin.f64 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 -7926335344172073/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (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.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 799388933858263/1125899906842624 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)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -7926335344172073/9007199254740992 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.f64 (sqrt.f64 #s(approx (+ (* (- 1 (cos (+ ky ky))) 1/2) (* (- 1 (cos (+ kx kx))) 1/2)) (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 799388933858263/1125899906842624 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)) #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 -5764607523034235/288230376151711744 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) th)) (/.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 ky ky))) #s(literal 1/2 binary64)))) (sin.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -5764607523034235/288230376151711744 binary64)) (/.f64 #s(approx (sin th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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 ky ky)))))) (sin.f64 ky))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #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 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (/.f64 (.f64 #s(approx (sin ky) (.f64 (fma.f64 (.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) 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))))) #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 -1152921504606847/1152921504606846976 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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))))) (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 3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) 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))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -1152921504606847/1152921504606846976 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3602879701896397/72057594037927936 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) 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))))) #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 3022314549036573/151115727451828646838272 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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 3022314549036573/151115727451828646838272 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 2486616182048933/248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 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 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (.f64 kx kx) kx)) #s(literal -1/2 binary64))) ky)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 2486616182048933/248661618204893321077691124073410420050228075398673858720231988446579748506266687766528 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 (/.f64 (.f64 (.f64 ky ky) (sin.f64 th)) (.f64 (.f64 kx kx) kx)) #s(literal -1/2 binary64))) 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 2894802230932905/28948022309329048855892746252171976963317496166410141009864396001978282409984 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 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 2894802230932905/28948022309329048855892746252171976963317496166410141009864396001978282409984 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 5890680864316837/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736 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))))
(if (<=.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) #s(literal 5890680864316837/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736 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)))

soundness1.7s (14.2%)

Memory

63.9MiB live, 1 620.5MiB allocated

Rules

14 278×	`lower-fma.f64`
14 278×	`lower-fma.f32`
11 410×	`lower-fma.f64`
11 410×	`lower-fma.f32`
9 304×	`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
0	75	446
0	126	434
1	382	433
0	2430	399
0	13	49
0	22	49
1	62	49
2	338	49
3	2902	49
0	8284	34
0	676	12982
1	2153	12249
2	7914	12231
0	8179	11789
0	878	16395
1	2795	15457
2	6669	15113
0	8987	14410
0	948	13964
1	3143	13509
0	8122	12790
0	75	495
0	123	483
1	416	351
0	3020	330

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

Compiler

Compiled 5 574 to 2 378 computations (57.3% saved)

preprocess206.0ms (1.7%)

Memory

-16.0MiB live, 374.9MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 3 996 to 530 computations (86.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated