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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze197.0ms (1.9%)

Memory

36.6MiB live, 305.4MiB 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)

sample2.4s (22.6%)

Memory

-2.4MiB live, 2 051.6MiB allocated

Samples

2.0s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-sin: 931.0ms (57.7% of total)

ival-pow2: 375.0ms (23.2% of total)

ival-add: 102.0ms (6.3% of total)

ival-div: 78.0ms (4.8% of total)

ival-mult: 61.0ms (3.8% of total)

ival-sqrt: 57.0ms (3.5% of total)

ival-true: 7.0ms (0.4% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

explain270.0ms (2.6%)

Memory

41.1MiB live, 352.9MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

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

Confusion

	Predicted +	Predicted -
+	11	1
-	0	244

Precision

1.0

Recall

0.9166666666666666

Confusion?

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

Precision?

1.0

Recall?

0.9166666666666666

Freqs

test

number	freq
0	245
1	11

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

88.0ms

512×

valid

Compiler

Compiled 152 to 43 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-sin: 36.0ms (57% of total)

ival-pow2: 10.0ms (15.8% of total)

ival-mult: 6.0ms (9.5% of total)

ival-sqrt: 4.0ms (6.3% of total)

ival-div: 3.0ms (4.7% of total)

ival-add: 2.0ms (3.2% of total)

ival-true: 1.0ms (1.6% of total)

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

exact: 0.0ms (0% of total)

preprocess106.0ms (1%)

Memory

-13.5MiB live, 64.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs

(*.f64 (/.f64 (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 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify3.0ms (0%)

Memory

6.1MiB live, 6.1MiB 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	7424	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

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

localize61.0ms (0.6%)

Memory

-8.3MiB live, 107.7MiB allocated

Localize:

Found 4 expressions of interest:

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

Samples

50.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-sin: 16.0ms (56.9% of total)

ival-pow2: 5.0ms (17.8% of total)

ival-div: 2.0ms (7.1% of total)

ival-mult: 2.0ms (7.1% of total)

ival-sqrt: 2.0ms (7.1% of total)

ival-add: 1.0ms (3.6% of total)

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

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

exact: 0.0ms (0% of total)

series42.0ms (0.4%)

Memory

-24.0MiB live, 69.1MiB 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 kx) #s(literal 2 binary64)) (patch (pow.f64 (sin.f64 kx) #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>) () ())

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
12.0ms	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 kx) 2) (pow (sin ky) 2))
5.0ms	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 kx) 2) (pow (sin ky) 2))
4.0ms	ky	@	0	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin kx) 2) (pow (sin ky) 2))
4.0ms	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 kx) 2) (pow (sin ky) 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 kx) 2) (pow (sin ky) 2))

simplify213.0ms (2%)

Memory

28.2MiB live, 250.9MiB allocated

Algorithm

1×	egg-herbie

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

rewrite496.0ms (4.7%)

Memory

-149.9MiB live, 263.6MiB allocated

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

Outputs
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eval110.0ms (1%)

Memory: 27.9MiB live, 147.4MiB allocated
Compiler: Compiled 10 166 to 1 715 computations (83.1% saved)

prune38.0ms (0.4%)

Memory

-18.2MiB live, 96.0MiB allocated

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	423	25	448
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	424	25	449

Accuracy

100.0%

Counts

449 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
	95.7%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	76.6%	(*.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (sin.f64 th))
	92.3%	(.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
▶	99.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
	70.3%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	72.1%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
	53.4%	(.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))
	59.4%	(.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))
	32.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
▶	38.3%	(.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))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	42.2%	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	99.5%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	76.3%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	26.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
	31.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
	43.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
▶	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 766 to 622 computations (18.8% saved)

simplify119.0ms (1.1%)

Memory

8.1MiB live, 87.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))
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 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64)))))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff	0	(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff	0	(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
cost-diff	448	(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (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))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	277
0	67	251
1	97	251
2	155	251
3	254	251
4	653	251
5	1303	251
6	2157	251
7	2544	251
8	2936	251
9	3119	251
10	3173	251
11	3229	251
12	3253	251
13	3255	251
14	3257	251
15	3329	251
16	3842	251
0	3842	251

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

localize125.0ms (1.2%)

Memory

-5.6MiB live, 309.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.12890625	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64)))))
accuracy	0.178066259768442	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	0.4552690430532607	(pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))
accuracy	2.8099071343070467	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))
accuracy	0.015625	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.11328125	(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
accuracy	0.15625	(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.19140625	(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
accuracy	0.0625	(fma.f64 (*.f64 #s(literal 1/2 binary64) kx) (/.f64 kx (sin.f64 ky)) (sin.f64 ky))
accuracy	0.11328125	(.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	0.12890625	(/.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	30.644755252230148	#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	29.50379559745233	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0	(sin.f64 kx)
accuracy	0.015625	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.11328125	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
accuracy	0.12890625	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Samples

69.0ms	197×	0	valid
31.0ms	59×	0	invalid

Compiler

Compiled 293 to 35 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-sin: 20.0ms (32.9% of total)

ival-mult: 11.0ms (18.1% of total)

ival-div: 7.0ms (11.5% of total)

ival-sqrt: 5.0ms (8.2% of total)

ival-hypot: 4.0ms (6.6% of total)

ival-pow2: 4.0ms (6.6% of total)

ival-add: 3.0ms (4.9% of total)

ival-pow: 3.0ms (4.9% of total)

ival-neg: 2.0ms (3.3% of total)

exact: 1.0ms (1.6% of total)

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

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

series86.0ms (0.8%)

Memory

31.1MiB live, 102.9MiB allocated

Counts

19 → 456

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

Calls

9 calls:

Time	Variable		Point	Expression
22.0ms	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))) (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (* (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin kx) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (pow (sqrt (sin ky)) 4) (pow (sin kx) 2))
3.0ms	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))) (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (* (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin kx) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (pow (sqrt (sin ky)) 4) (pow (sin kx) 2))
3.0ms	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))) (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (* (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin kx) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (pow (sqrt (sin ky)) 4) (pow (sin kx) 2))
3.0ms	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))) (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (* (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin kx) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (pow (sqrt (sin ky)) 4) (pow (sin kx) 2))
2.0ms	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))) (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (* (* (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (neg (sin ky))) (sin th)) (/ -1 (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin kx) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (pow (sqrt (sin ky)) 4) (pow (sin kx) 2))

simplify226.0ms (2.1%)

Memory

-0.3MiB live, 369.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	425	10037
1	1364	9781
2	5255	9480
0	8366	8927

Stop Event

1×	iter limit
1×	node limit

Counts

456 → 453

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))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ -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 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 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 (/ 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))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (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))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/2 (/ (pow kx 2) (sin ky)))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/2 (/ (pow kx 2) (sin ky)))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 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))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ 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 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))))
(/ -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 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 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 (/ 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 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))))))
(* 1/2 (/ (pow kx 2) ky))
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* 1/12 (pow kx 2))))) ky)
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) 1/6)))))) ky)
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (+ (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) (* (pow ky 2) (+ 1/120 (* -1/2 (+ (* -1/5040 (pow kx 2)) (+ (* 1/720 (pow kx 2)) (* 1/6 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))))))))) 1/6)))))) ky)
(pow ky 2)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (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) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)

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 #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 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (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)))
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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) 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 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 #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 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (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)
(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 #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 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (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)))
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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin 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 #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 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (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)))
(/ -1 (sin ky))
(/.f64 #s(literal -1 binary64) (sin.f64 ky))
(- (* 1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) kx) kx (/.f64 #s(literal -1 binary64) (sin.f64 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)))
(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)))) (sin.f64 ky)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) (.f64 kx kx) (/.f64 #s(literal -1 binary64) (sin.f64 ky)))
(- (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))) (* 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 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (.f64 (sin.f64 ky) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (.f64 (+.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)))) #s(literal -1/2 binary64)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 3 binary64))) kx) kx (/.f64 #s(literal -1 binary64) (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 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 #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 (pow.f64 kx #s(literal 4 binary64)) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th))))) (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)))
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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
(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) (* 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) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(pow kx 2)
(*.f64 kx kx)
(* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx))
(* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt (+ (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
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(* 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
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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 (+ (* -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 (+ (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 th)
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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)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(/ (* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (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))))) #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)))) #s(literal -1/12 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(/ 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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/2 binary64) (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 #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 (/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 ky (sin.f64 kx)))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) ky)
(sin 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))))))
(fma.f64 (fma.f64 (/.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))
(+ (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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(/ (* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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 (fma.f64 (.f64 (sin.f64 kx) (sin.f64 th)) (fma.f64 (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))))) #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)))) #s(literal -1/12 binary64))) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/5040 binary64) (/.f64 #s(literal -1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th))))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (*.f64 ky ky) (/.f64 (sin.f64 th) (sin.f64 kx))) ky)
(/ 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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/2 binary64) (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 #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 (/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 ky (sin.f64 kx)))
(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))))))
(fma.f64 (fma.f64 (/.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))
(+ (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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) 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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/2 binary64) (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 #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 (/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 ky (sin.f64 kx)))
(/ (* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ -1 (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 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) ky) ky (/.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 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 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 (/ 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/2 binary64) (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 #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 (/.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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 ky (sin.f64 kx)))
(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))))))
(fma.f64 (fma.f64 (/.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))
(+ (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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 ky (/.f64 ky (sin.f64 kx)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(* 1/2 (/ (pow kx 2) ky))
(.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* 1/12 (pow kx 2))))) ky)
(/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) 1/6)))))) ky)
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(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (+ (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) (* (pow ky 2) (+ 1/120 (* -1/2 (+ (* -1/5040 (pow kx 2)) (+ (* 1/720 (pow kx 2)) (* 1/6 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))))))))) 1/6)))))) ky)
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal -31/15120 binary64)) #s(literal -1/2 binary64) #s(literal 1/120 binary64)) ky) ky (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64))) (.f64 ky ky) (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (*.f64 ky ky))) ky)
(pow ky 2)
(*.f64 ky ky)
(* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))
(fma.f64 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 ky ky) #s(literal 2/45 binary64) #s(literal -1/3 binary64)) (.f64 ky ky))
(* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))
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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) (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) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* -1 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt (+ (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) (* 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) (* 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) (* 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) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) 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))

rewrite115.0ms (1.1%)

Memory

6.3MiB live, 202.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	214
0	67	169
1	211	169
2	1126	169
0	9302	169

Stop Event

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

Counts

19 → 559

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

Outputs
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eval326.0ms (3.1%)

Memory: -25.5MiB live, 368.7MiB allocated
Compiler: Compiled 31 694 to 3 074 computations (90.3% saved)

prune347.0ms (3.3%)

Memory

-2.0MiB live, 160.7MiB allocated

Pruning

34 alts after pruning (31 fresh and 3 done)

	Pruned	Kept	Total
New	1 450	19	1 469
Fresh	8	12	20
Picked	2	3	5
Done	0	0	0
Total	1 460	34	1 494

Accuracy

100.0%

Counts

1 494 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
	95.7%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	76.6%	(*.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (sin.f64 th))
	92.3%	(.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	74.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #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))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
	53.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.f64 ky ky))))) (sin.f64 th))
	62.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
	59.4%	(.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))
▶	32.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
▶	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
✓	38.3%	(.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))
	22.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
	25.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
	12.5%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	42.2%	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	38.3%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	31.4%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	34.1%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	76.3%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	26.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	31.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	26.0%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
▶	43.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	16.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
	16.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
▶	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))

Compiler

Compiled 1 053 to 852 computations (19.1% saved)

simplify15.0ms (0.1%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(sin.f64 ky)
cost-diff	0	(*.f64 (sin.f64 ky) th)
cost-diff	0	(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
cost-diff	0	(pow.f64 th #s(literal 3 binary64))
cost-diff	0	(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
cost-diff	0	#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff	0	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
cost-diff	0	(sin.f64 th)
cost-diff	384	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	346
0	81	341
1	115	341
2	153	341
3	175	341
4	182	341
5	188	341
6	188	341
7	228	341
8	228	341
9	275	341
10	307	341
11	357	341
12	361	341
0	361	341

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize176.0ms (1.7%)

Memory

-10.9MiB live, 194.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.19921875	(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	2.7055487376473097	(.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
accuracy	3.1643064545842825	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	25.040665146889573	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
accuracy	0.11328125	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
accuracy	0.12890625	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))))
accuracy	0.22265625	(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky)
accuracy	32.04198510021335	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
accuracy	0	(sin.f64 kx)
accuracy	0.11328125	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
accuracy	0.12890625	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
accuracy	31.365634395542596	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))
accuracy	0	(pow.f64 th #s(literal 3 binary64))
accuracy	0.0390625	(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
accuracy	25.2789874682436	#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
accuracy	29.50379559745233	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
accuracy	0	(sin.f64 kx)
accuracy	0.015625	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.08984375	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
accuracy	0.09994125976844201	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Samples

99.0ms	197×	0	valid
43.0ms	59×	0	invalid

Compiler

Compiled 298 to 42 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 119.0ms

ival-sin: 37.0ms (31.1% of total)

ival-pow: 32.0ms (26.9% of total)

ival-mult: 11.0ms (9.2% of total)

ival-sqrt: 10.0ms (8.4% of total)

ival-div: 9.0ms (7.6% of total)

ival-add: 5.0ms (4.2% of total)

ival-hypot: 5.0ms (4.2% of total)

ival-pow2: 5.0ms (4.2% of total)

const: 4.0ms (3.4% of total)

exact: 1.0ms (0.8% of total)

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

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

series72.0ms (0.7%)

Memory

18.8MiB live, 175.3MiB allocated

Counts

22 → 528

Calls

Call 1

Inputs
#s(alt (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (patch (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (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)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) (patch #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)) #<representation binary64>) () ())
#s(alt (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) (patch (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th) #<representation binary64>) () ())
#s(alt (pow.f64 th #s(literal 3 binary64)) (patch (pow.f64 th #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (patch (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (patch #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (patch (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))) (patch #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx))) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (patch (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) #<representation binary64>) () ())
#s(alt (.f64 (sin.f64 ky) th) (patch (.f64 (sin.f64 ky) th) #<representation binary64>) () ())
#s(alt (sin.f64 kx) (patch (sin.f64 kx) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (patch (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
11.0ms	ky	@	-inf	((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (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) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (sin kx) (* (/ 1/2 (sin kx)) ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))
8.0ms	kx	@	-inf	((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (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) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (sin kx) (* (/ 1/2 (sin kx)) ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))
5.0ms	ky	@	0	((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (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) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (sin kx) (* (/ 1/2 (sin kx)) ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))
4.0ms	ky	@	inf	((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (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) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (sin kx) (* (/ 1/2 (sin kx)) ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))
4.0ms	kx	@	0	((/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (sin th) (/ (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) (+ (* (pow th 3) -1/6) th) (pow th 3) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (* (sin ky) th) (sin kx) (* (/ 1/2 (sin kx)) ky) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))

simplify214.0ms (2%)

Memory

-18.8MiB live, 295.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	554	10648
1	1822	10338
2	7378	10294
0	8052	9624

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 522

Calls

Call 1

Inputs
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(* 1/2 (/ ky kx))
(/ (+ (* 1/12 (* (pow kx 2) ky)) (* 1/2 ky)) kx)
(/ (+ (* 1/2 ky) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ (* -1/36 ky) (* 1/120 ky)))) (* 1/12 ky)))) kx)
(/ (+ (* 1/2 ky) (* (pow kx 2) (+ (* 1/12 ky) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ (* -1/5040 ky) (+ (* 1/720 ky) (* 1/6 (+ (* -1/36 ky) (* 1/120 ky))))))) (* -1/2 (+ (* -1/36 ky) (* 1/120 ky)))))))) kx)
(/ 1 (sin ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (sin ky) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 3))))) (/ 1 (sin ky)))
(/ 1 (pow (sin ky) 2))
(+ (* -1 (/ (pow kx 2) (pow (sin ky) 4))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6)))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(+ (* (pow kx 2) (- (* (pow kx 2) (+ (* -1 (* (pow kx 2) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (/ 1 (pow (sin ky) 6))))) (/ 1 (pow (sin ky) 4)))) (/ 1 (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(pow th 3)
(pow th 3)
(pow th 3)
(pow th 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 (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* -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))
(pow th 3)
(pow th 3)
(pow th 3)
(pow th 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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* -1/6 (pow th 3))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
(pow th 3)
(pow th 3)
(pow th 3)
(pow th 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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky th) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (* -1/6 (/ th (sin kx))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
(* ky th)
(* ky (+ th (* -1/6 (* (pow ky 2) th))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* 1/120 (* (pow ky 2) th))))))
(* ky (+ th (* (pow ky 2) (+ (* -1/6 th) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) th)) (* 1/120 th)))))))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(/ 1 (sin kx))
(+ (* -1/2 (/ (pow ky 2) (pow (sin kx) 3))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* 1/2 (* (pow ky 2) (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))) (* 1/2 (/ 1 (pow (sin kx) 3))))) (/ 1 (sin kx)))
(/ 1 (pow (sin kx) 2))
(+ (* -1 (/ (pow ky 2) (pow (sin kx) 4))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6)))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(+ (* (pow ky 2) (- (* (pow ky 2) (+ (* -1 (* (pow ky 2) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (/ 1 (pow (sin kx) 6))))) (/ 1 (pow (sin kx) 4)))) (/ 1 (pow (sin kx) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* th (sin ky))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(* 1/2 (/ ky (sin kx)))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))

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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #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 #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) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (/.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) (/.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 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (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 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #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)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) 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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) 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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin 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))))))
(fma.f64 (fma.f64 (/.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 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 (pow.f64 kx #s(literal 4 binary64)) (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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) 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 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 #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 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
th
(+ th (* -1/2 (/ (* (pow kx 2) th) (pow (sin ky) 2))))
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) th) (.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 (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (.f64 kx kx) th)
(+ th (* (pow kx 2) (+ (* -1/2 (/ th (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* th (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* th (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) th)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) th) (.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 (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64))) (.f64 kx kx) th)
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
(* 1/2 (/ ky kx))
(*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))
(/ (+ (* 1/12 (* (pow kx 2) ky)) (* 1/2 ky)) kx)
(/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)
(/ (+ (* 1/2 ky) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ (* -1/36 ky) (* 1/120 ky)))) (* 1/12 ky)))) kx)
(/.f64 (fma.f64 (fma.f64 (.f64 (.f64 ky #s(literal 7/720 binary64)) kx) kx (.f64 #s(literal 1/12 binary64) ky)) (.f64 kx kx) (*.f64 #s(literal 1/2 binary64) ky)) kx)
(/ (+ (* 1/2 ky) (* (pow kx 2) (+ (* 1/12 ky) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (+ (* -1/5040 ky) (+ (* 1/720 ky) (* 1/6 (+ (* -1/36 ky) (* 1/120 ky))))))) (* -1/2 (+ (* -1/36 ky) (* 1/120 ky)))))))) kx)
(/.f64 (fma.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 ky #s(literal 1/840 binary64) (.f64 ky #s(literal -7/2160 binary64)))) (.f64 kx kx) (.f64 ky #s(literal 7/720 binary64))))) kx)
(/ 1 (sin ky))
(/.f64 #s(literal 1 binary64) (sin.f64 ky))
(+ (* -1/2 (/ (pow kx 2) (pow (sin ky) 3))) (/ 1 (sin ky)))
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 3 binary64)))) #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 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)))
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(+ (* (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)))
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(sin kx)
(sin.f64 kx)
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(sin.f64 kx)
(sin kx)
(sin.f64 kx)
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(* 1/2 (/ ky (sin kx)))
(*.f64 (/.f64 ky (sin.f64 kx)) #s(literal 1/2 binary64))
(* 1/2 (/ ky (sin kx)))
(*.f64 (/.f64 ky (sin.f64 kx)) #s(literal 1/2 binary64))
(* 1/2 (/ ky (sin kx)))
(*.f64 (/.f64 ky (sin.f64 kx)) #s(literal 1/2 binary64))
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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
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(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
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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)))))))
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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
(* th (+ 1 (* -1/6 (pow th 2))))
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(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
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(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
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th
(* th (+ 1 (* -1/6 (pow th 2))))
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(* th (+ 1 (* -1/6 (pow th 2))))
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(* th (+ 1 (* -1/6 (pow th 2))))
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(* (* 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 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))))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (sin.f64 ky) (.f64 (pow.f64 th #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(* 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/5040 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 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))))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (sin.f64 ky) (.f64 (pow.f64 th #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(* 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/5040 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 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))))))))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (sin.f64 ky) (.f64 (pow.f64 th #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal 1/120 binary64) (.f64 #s(literal -1/6 binary64) (sin.f64 ky))))))
(* 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/6 binary64) (sin.f64 ky)) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (fma.f64 #s(literal 1/120 binary64) (sin.f64 ky) (.f64 (.f64 (.f64 (sin.f64 ky) th) th) #s(literal -1/5040 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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(* (* th (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)))))
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(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* th (sin ky))
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(* th (sin ky))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin.f64 th)
(sin th)
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(sin th)
(sin.f64 th)
(sin th)
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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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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 (pow.f64 th #s(literal 3 binary64)) #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)) (pow.f64 th #s(literal 3 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)) (pow.f64 th #s(literal 3 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)) (pow.f64 th #s(literal 3 binary64)))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
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(pow.f64 th #s(literal 3 binary64))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(pow th 3)
(pow.f64 th #s(literal 3 binary64))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (* (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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(* (* th (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)))))
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(* (* th (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)))))
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(* th (sin ky))
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(* th (sin ky))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin th)
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
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(sin th)
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(sin.f64 th)
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(* -1/6 (pow th 3))
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(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(* -1 (* (pow th 3) (- 1/6 (/ 1 (pow th 2)))))
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(pow th 3)
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(pow th 3)
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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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(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (fma.f64 (.f64 (.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (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 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (.f64 ky ky) (fma.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 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 (sin.f64 th) (/.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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.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 (sin.f64 kx) #s(literal -1/2 binary64)) (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 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) ky)
(sin 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))))))
(fma.f64 (fma.f64 (/.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))
(+ (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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (.f64 ky ky) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (sin.f64 kx)) (/.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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(/ (* 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 #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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.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 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 (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))) (* (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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal 1/120 binary64) (fma.f64 (fma.f64 (.f64 (.f64 (sin.f64 kx) #s(literal -1/2 binary64)) (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 #s(literal -1/5040 binary64) (sin.f64 th)) (sin.f64 kx))))) (.f64 ky ky) (fma.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 (.f64 #s(literal 1/12 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))))) (.f64 ky ky) (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) #s(literal -1/6 binary64) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 (sin.f64 th) (/.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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.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 (sin.f64 kx) #s(literal -1/2 binary64)) (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 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx)))) (/.f64 ky (sin.f64 kx)))
(sin 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))))))
(fma.f64 (fma.f64 (/.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))
(+ (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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (.f64 ky ky) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (sin.f64 kx)) (/.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))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(/ (* 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))))))) (* (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 th) (sin kx))
(*.f64 (/.f64 th (sin.f64 kx)) ky)
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ th (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ th (pow (sin kx) 3))) (+ (* -1/6 (/ th (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ th (sin kx))) (+ (* 1/12 (/ th (pow (sin kx) 3))) (+ (* 1/2 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* th (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* th (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ th (pow (sin kx) 3))) (* -1/5040 (/ th (sin kx)))))))))))))) (/ th (sin kx))))
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(* ky th)
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(/ 1 (sin kx))
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(/ 1 (pow (sin kx) 2))
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(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

rewrite137.0ms (1.3%)

Memory

19.7MiB live, 260.2MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	285
0	81	223
1	266	219
2	1409	215
0	9126	215

Stop Event

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

Counts

22 → 425

Calls

Call 1

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

Outputs
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eval182.0ms (1.7%)

Memory: 6.7MiB live, 498.6MiB allocated
Compiler: Compiled 25 049 to 2 734 computations (89.1% saved)

prune176.0ms (1.7%)

Memory

3.3MiB live, 379.1MiB allocated

Pruning

66 alts after pruning (61 fresh and 5 done)

	Pruned	Kept	Total
New	1 208	39	1 247
Fresh	4	22	26
Picked	3	2	5
Done	0	3	3
Total	1 215	66	1 281

Accuracy

100.0%

Counts

1 281 → 66

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
	95.7%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	24.5%	(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
▶	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky)))
✓	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
▶	38.3%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
	34.1%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
	31.9%	(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	24.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (sin.f64 th))))
	76.6%	(*.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (sin.f64 th))
	92.3%	(.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	29.4%	(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
	16.7%	(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	31.4%	(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
	74.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #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))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
	53.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.f64 ky ky))))) (sin.f64 th))
	62.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
	59.4%	(.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))
	28.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
	33.1%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
	28.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
	43.3%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
✓	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
▶	25.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
✓	38.3%	(.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))
	25.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
▶	12.5%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	42.2%	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	31.4%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	34.1%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	24.4%	(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
	31.4%	(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
	76.3%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	31.3%	(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
	26.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	31.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	5.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
	6.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
	6.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
	45.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
	14.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
	22.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	19.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
	21.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	14.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
	16.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	16.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 binary64) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 th #s(literal -1/6 binary64)) th)))
▶	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
	13.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
	16.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
	13.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
	11.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
	7.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))

Compiler

Compiled 1 777 to 1 532 computations (13.8% saved)

simplify23.0ms (0.2%)

Memory

-7.8MiB live, 30.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
cost-diff	0	(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky))
cost-diff	0	(sin.f64 th)
cost-diff	0	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
cost-diff	0	(*.f64 th th)
cost-diff	0	(.f64 #s(literal -1/6 binary64) (.f64 th th))
cost-diff	0	#s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th))
cost-diff	0	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
cost-diff	0	(/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky))
cost-diff	0	(sin.f64 th)
cost-diff	384	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky)))
cost-diff	7168	(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	495
0	105	485
1	168	434
2	279	431
3	370	431
4	398	431
5	438	431
6	438	431
7	544	431
8	570	431
9	594	431
0	594	428

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize168.0ms (1.6%)

Memory

-17.6MiB live, 348.3MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.08984375	(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky))
accuracy	0.09994125976844201	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
accuracy	0.16015625	(*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx)
accuracy	30.644755252230148	#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
accuracy	0.12890625	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx))))
accuracy	0.25910040151587455	(fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64))
accuracy	22.53141925937145	#s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx))
accuracy	31.365634395542596	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)))
accuracy	0.12890625	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64)))))
accuracy	5.738549380640215	(/.f64 (*.f64 kx kx) ky)
accuracy	20.836093701257074	#s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64)))
accuracy	30.644755252230148	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))
accuracy	0.04296875	(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)
accuracy	0.1484375	(.f64 #s(literal -1/6 binary64) (.f64 th th))
accuracy	25.2789874682436	#s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th))
accuracy	29.50379559745233	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
accuracy	0.08984375	(/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky))
accuracy	0.09994125976844201	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky)))
accuracy	0.10546875	(pow.f64 (sin.f64 kx) #s(literal -1 binary64))
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))

Samples

97.0ms	197×	0	valid
30.0ms	59×	0	invalid

Compiler

Compiled 356 to 55 computations (84.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-mult: 21.0ms (20.9% of total)

ival-sin: 19.0ms (18.9% of total)

ival-div: 15.0ms (14.9% of total)

ival-hypot: 11.0ms (10.9% of total)

ival-add: 8.0ms (8% of total)

const: 8.0ms (8% of total)

ival-pow: 8.0ms (8% of total)

ival-sqrt: 5.0ms (5% of total)

ival-pow2: 4.0ms (4% of total)

exact: 1.0ms (1% of total)

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

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

series60.0ms (0.6%)

Memory

5.6MiB live, 125.0MiB allocated

Counts

25 → 540

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64))) (patch (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (sin.f64 th) (patch (sin.f64 th) #<representation binary64>) () ())
#s(alt (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky)) (patch (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal -1 binary64)))) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th))) (patch #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th))) #<representation binary64>) () ())
#s(alt #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)) (patch #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal -1/6 binary64) (.f64 th th)) (patch (.f64 #s(literal -1/6 binary64) (.f64 th th)) #<representation binary64>) () ())
#s(alt (.f64 th th) (patch (.f64 th th) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (patch (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #<representation binary64>) () ())
#s(alt (sin.f64 ky) (patch (sin.f64 ky) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64)))) (patch #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th)) (patch (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th)) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (patch (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx))) (patch #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx))) #<representation binary64>) () ())
#s(alt (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky))) (patch (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)) (patch (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (patch #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) #<representation binary64>) () ())
#s(alt (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) (patch (pow.f64 (sin.f64 kx) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th) (patch (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th) #<representation binary64>) () ())
#s(alt #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))) (patch #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (.f64 kx kx) ky) (patch (/.f64 (.f64 kx kx) ky) #<representation binary64>) () ())
#s(alt #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)) (patch #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (patch (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) (patch (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) #<representation binary64>) () ())

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	th	@	inf	((/ 1 (pow (sin kx) -1)) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th 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))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin kx) -1) (+ (* (* -1/6 (* th th)) th) th) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/ (* kx kx) ky) (sin kx) (+ (* 1/120 (* kx kx)) -1/6) (* (/ 1/2 (sin ky)) kx))
4.0ms	kx	@	inf	((/ 1 (pow (sin kx) -1)) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th 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))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin kx) -1) (+ (* (* -1/6 (* th th)) th) th) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/ (* kx kx) ky) (sin kx) (+ (* 1/120 (* kx kx)) -1/6) (* (/ 1/2 (sin ky)) kx))
4.0ms	kx	@	-inf	((/ 1 (pow (sin kx) -1)) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th 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))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin kx) -1) (+ (* (* -1/6 (* th th)) th) th) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/ (* kx kx) ky) (sin kx) (+ (* 1/120 (* kx kx)) -1/6) (* (/ 1/2 (sin ky)) kx))
4.0ms	ky	@	-inf	((/ 1 (pow (sin kx) -1)) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th 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))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin kx) -1) (+ (* (* -1/6 (* th th)) th) th) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/ (* kx kx) ky) (sin kx) (+ (* 1/120 (* kx kx)) -1/6) (* (/ 1/2 (sin ky)) kx))
4.0ms	ky	@	inf	((/ 1 (pow (sin kx) -1)) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th 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))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (pow (sin kx) -1) (+ (* (* -1/6 (* th th)) th) th) (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/ (* kx kx) ky) (sin kx) (+ (* 1/120 (* kx kx)) -1/6) (* (/ 1/2 (sin ky)) kx))

simplify182.0ms (1.7%)

Memory

-8.8MiB live, 269.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	10008
1	1476	9664
2	5509	9307
0	8160	8620

Stop Event

1×	iter limit
1×	node limit

Counts

540 → 534

Calls

Call 1

Inputs
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))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin 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 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(/ 1 kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
-1/6
(- (* 1/120 (pow kx 2)) 1/6)
(- (* 1/120 (pow kx 2)) 1/6)
(- (* 1/120 (pow kx 2)) 1/6)
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (sin kx))
(/ 1 (sin kx))
(/ 1 (sin kx))
(/ 1 (sin kx))
(* 1/2 (/ (pow kx 2) (sin ky)))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/120 (pow kx 2))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(/ 1 (sin kx))
(/ 1 (sin kx))
(/ 1 (sin kx))
(/ 1 (sin kx))
(* 1/2 (/ (pow kx 2) (sin ky)))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(* (pow kx 2) (+ (* 1/2 (/ 1 (sin ky))) (/ (sin ky) (pow kx 2))))
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* 1/120 (pow kx 2))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* (pow kx 2) (- 1/120 (* 1/6 (/ 1 (pow kx 2)))))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
th
(* th (+ 1 (* -1/6 (pow th 2))))
(* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))
(* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(pow th 2)
(pow th 2)
(pow th 2)
(pow th 2)
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))))
(* (* th (sin ky)) (sqrt (/ 1 (+ (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 (* -1/6 (pow th 2))))
(* th (+ 1 (* -1/6 (pow th 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(pow th 2)
(pow th 2)
(pow th 2)
(pow th 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/6 (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))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(* -1/6 (pow th 2))
(pow th 2)
(pow th 2)
(pow th 2)
(pow th 2)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* -1/6 (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)))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ (sin kx) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (* 1/2 (/ 1 (sin kx)))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(* 1/2 (/ (pow kx 2) ky))
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* 1/12 (pow kx 2))))) ky)
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) 1/6)))))) ky)
(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* 1/12 (pow kx 2)) (* (pow ky 2) (- (+ (* -1/2 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))) (* (pow ky 2) (+ 1/120 (* -1/2 (+ (* -1/5040 (pow kx 2)) (+ (* 1/720 (pow kx 2)) (* 1/6 (+ (* -1/36 (pow kx 2)) (* 1/120 (pow kx 2)))))))))) 1/6)))))) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(* 1/2 (/ kx ky))
(/ (+ (* 1/12 (* kx (pow ky 2))) (* 1/2 kx)) ky)
(/ (+ (* 1/2 kx) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (+ (* -1/36 kx) (* 1/120 kx)))) (* 1/12 kx)))) ky)
(/ (+ (* 1/2 kx) (* (pow ky 2) (+ (* 1/12 kx) (* (pow ky 2) (+ (* -1/2 (* (pow ky 2) (+ (* -1/5040 kx) (+ (* 1/720 kx) (* 1/6 (+ (* -1/36 kx) (* 1/120 kx))))))) (* -1/2 (+ (* -1/36 kx) (* 1/120 kx)))))))) ky)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(/ (pow kx 2) ky)
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))
(* 1/2 (/ kx (sin ky)))

Outputs
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (/.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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.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) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) kx (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (/.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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
(sin th)
(sin.f64 th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (/.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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.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) (- (* 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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) 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 -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(+ (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 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) 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 #s(literal -1/2 binary64) (.f64 kx kx)) (/.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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.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) (- (* 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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) 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 -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(+ (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 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) 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 #s(literal -1/2 binary64) (.f64 kx kx)) (/.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 #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 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(fma.f64 (/.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) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) kx) kx (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) 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 -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(+ (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 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky)))
(/ 1 kx)
(/.f64 #s(literal 1 binary64) kx)
(/ (+ 1 (* 1/6 (pow kx 2))) kx)
(/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* 7/360 (pow kx 2))))) kx)
(/.f64 (fma.f64 (fma.f64 #s(literal 7/360 binary64) (.f64 kx kx) #s(literal 1/6 binary64)) (.f64 kx kx) #s(literal 1 binary64)) kx)
(/ (+ 1 (* (pow kx 2) (+ 1/6 (* (pow kx 2) (+ 7/360 (* 31/15120 (pow kx 2))))))) kx)
(/.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 31/15120 binary64) (.f64 kx kx) #s(literal 7/360 binary64)) (.f64 kx kx) #s(literal 1/6 binary64)) (*.f64 kx kx) #s(literal 1 binary64)) kx)
(sin ky)
(sin.f64 ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
kx
(* kx (+ 1 (* -1/6 (pow kx 2))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
-1/6
#s(literal -1/6 binary64)
(- (* 1/120 (pow kx 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64))
(- (* 1/120 (pow kx 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64))
(- (* 1/120 (pow kx 2)) 1/6)
(fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(sin kx)
(sin.f64 kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
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(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (+ (* 1/12 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 31/15120 (sin kx)) (+ (* 7/720 (/ 1 (sin kx))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (sin kx))))))))))))))) ky)
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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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
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(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
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(/ (* ky (sin th)) (sin kx))
(*.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx)))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal 1/120 binary64)) (.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sin.f64 th)))) (.f64 ky ky) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (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)))) (.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)))) (.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 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 (neg.f64 (pow.f64 ky #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))) (/.f64 #s(literal 1/6 binary64) (sin.f64 kx))) (/.f64 ky (sin.f64 kx)))
(* 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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (.f64 (sin.f64 kx) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 #s(literal 1/12 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64)))) (/.f64 #s(literal 1/120 binary64) (sin.f64 kx))) (.f64 ky ky) (-.f64 (/.f64 #s(literal -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.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 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (+.f64 (fma.f64 (fma.f64 (sin.f64 kx) (fma.f64 #s(literal -1/12 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (.f64 #s(literal -1/2 binary64) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))) (-.f64 (/.f64 #s(literal -1/5040 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/240 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (.f64 ky ky) (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 -1/6 binary64) (sin.f64 kx)) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 3 binary64))))) (/.f64 ky (sin.f64 kx)))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) #s(literal -1/6 binary64) ky)
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (*.f64 ky ky) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) ky)
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) (.f64 ky ky) #s(literal -1/6 binary64)) ky)
(sin 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))))))
(fma.f64 (.f64 (fma.f64 (/.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))) 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 (pow.f64 ky #s(literal 4 binary64)) (fma.f64 (.f64 (.f64 ky ky) #s(literal 1/2 binary64)) (/.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)))) (sin.f64 kx)) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 kx))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))
(/ (* 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))))
(fma.f64 (pow.f64 ky #s(literal 3 binary64)) (.f64 (/.f64 (sin.f64 th) (sin.f64 kx)) (+.f64 #s(literal -1/6 binary64) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (/.f64 ky (sin.f64 kx))))
(* 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))
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(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
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(sin kx)
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(+ (sin kx) (* 1/2 (/ (pow ky 2) (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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(/ (+ (sin kx) (* (pow ky 2) (+ (* 1/6 (sin kx)) (+ (* 1/2 (/ 1 (sin kx))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (+ (* 7/360 (sin kx)) (* 1/12 (/ 1 (sin kx)))))))))) ky)
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(sin kx)
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(* 1/2 (/ (pow kx 2) ky))
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(/ (+ (* 1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* 1/12 (pow kx 2))))) ky)
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(/ (+ (* 1/12 (* kx (pow ky 2))) (* 1/2 kx)) ky)
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(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(sqrt (+ (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (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) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (sin.f64 th)))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
(* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 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))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(fma.f64 (*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64)) kx (sin.f64 ky))
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(/ (pow kx 2) ky)
(/.f64 (*.f64 kx kx) ky)
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))
(* 1/2 (/ kx (sin ky)))
(*.f64 (/.f64 kx (sin.f64 ky)) #s(literal 1/2 binary64))

rewrite204.0ms (1.9%)

Memory

14.5MiB live, 247.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	410
0	105	365
1	388	332
2	2420	332
0	8689	329

Stop Event

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

Counts

25 → 308

Calls

Call 1

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

Outputs
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eval135.0ms (1.3%)

Memory: 9.1MiB live, 275.1MiB allocated
Compiler: Compiled 19 866 to 2 019 computations (89.8% saved)

prune141.0ms (1.3%)

Memory

16.8MiB live, 213.3MiB allocated

Pruning

78 alts after pruning (73 fresh and 5 done)

	Pruned	Kept	Total
New	964	22	986
Fresh	5	51	56
Picked	4	1	5
Done	1	4	5
Total	974	78	1 052

Accuracy

100.0%

Counts

1 052 → 78

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.7%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	12.5%	(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
	23.1%	(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
	24.5%	(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) (sin.f64 ky)))
	63.2%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))
	63.9%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky)))
✓	99.7%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	32.6%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
	38.7%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
	34.1%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
	99.5%	(/.f64 (sin.f64 th) (*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	31.9%	(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
	99.5%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	24.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (sin.f64 th))))
	23.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
	76.6%	(*.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (sin.f64 th))
	92.3%	(.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))
	29.4%	(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
	16.7%	(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	31.4%	(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
	74.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #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))
	72.3%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
	53.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.f64 ky ky))))) (sin.f64 th))
	62.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
	59.4%	(.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))
	28.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
	33.1%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
	28.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
	43.3%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
✓	34.1%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
	25.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
	15.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
	15.3%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
	24.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
	25.2%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
	10.8%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
	10.9%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
	12.8%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
	99.6%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	42.2%	(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	31.4%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	34.1%	(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
	24.4%	(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
	31.4%	(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
	76.3%	(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	12.5%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
	31.3%	(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
	26.0%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
	31.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	45.8%	#s(approx (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
	5.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
	6.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
	6.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
	14.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
	22.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	19.9%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
	23.1%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
	21.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
	14.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
	16.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
✓	31.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	16.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 binary64) th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 th #s(literal -1/6 binary64)) th)))
✓	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
	16.6%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
	13.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
	16.5%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
	13.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
	11.3%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
	7.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))

Compiler

Compiled 2 771 to 1 459 computations (47.3% saved)

regimes351.0ms (3.3%)

Memory

-3.0MiB live, 517.8MiB allocated

Counts

106 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))
(*.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 ky) (sin.f64 kx))) (sin.f64 ky))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 th (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 th th) #s(literal 1 binary64)) (sin.f64 ky))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
#s(approx (/ (sin th) (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) th) (.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (sin.f64 ky))))
(/.f64 (sin.f64 th) (*.f64 (pow.f64 (sin.f64 ky) #s(literal -1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.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 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 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 (sqrt.f64 (sin.f64 ky)) #s(literal 4 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (sqrt.f64 (sin.f64 ky)) (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
(*.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (sin.f64 th))
(.f64 (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (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 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64)))

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

Calls

9 calls:

67.0ms	kx
50.0ms	(sin.f64 kx)
36.0ms	th
34.0ms	(/.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)))))
33.0ms	(sin.f64 ky)

Results

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

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes219.0ms (2.1%)

Memory

4.2MiB live, 297.1MiB allocated

Counts

81 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th))

Outputs

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

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

Calls

9 calls:

32.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
26.0ms	(sin.f64 th)
24.0ms	(sin.f64 kx)
23.0ms	kx
23.0ms	th

Results

Accuracy	Segments	Branch
99.4%	2	`kx`
94.6%	2	`ky`
79.1%	3	`th`
85.2%	5	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
99.5%	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)))))`
94.6%	3	`(sin.f64 ky)`
99.3%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
99.4%	3	`(sin.f64 kx)`
72.3%	1	`(sin.f64 th)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes141.0ms (1.3%)

Memory

-27.5MiB live, 209.9MiB allocated

Counts

80 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (*.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky)))

Outputs

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

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

Calls

6 calls:

25.0ms	ky
23.0ms	kx
23.0ms	(sin.f64 ky)
22.0ms	(sin.f64 kx)
22.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
81.4%	3	`(sin.f64 ky)`
81.2%	2	`ky`
85.8%	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)))))`
85.5%	3	`(sin.f64 kx)`
85.4%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
85.2%	2	`kx`

Compiler

Compiled 23 to 31 computations (-34.8% saved)

regimes48.0ms (0.5%)

Memory

4.6MiB live, 80.0MiB allocated

Counts

79 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 #s(approx ( (sin ky) th) (.f64 (.f64 (fma.f64 (*.f64 ky ky) #s(literal -1/6 binary64) #s(literal 1 binary64)) th) ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))

Outputs

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

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

Calls

2 calls:

23.0ms	kx
20.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
85.2%	2	`kx`
85.2%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`

Compiler

Compiled 5 to 9 computations (-80% saved)

regimes154.0ms (1.5%)

Memory

42.1MiB live, 155.9MiB allocated

Counts

77 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (neg.f64 (sin.f64 ky))) (sin.f64 th))

Outputs

(*.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) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))

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

Calls

5 calls:

63.0ms	(/.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)))))
25.0ms	ky
22.0ms	kx
21.0ms	(sin.f64 kx)
19.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
78.2%	2	`ky`
80.7%	3	`(sin.f64 kx)`
82.6%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
80.7%	2	`kx`
80.7%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`

Compiler

Compiled 21 to 27 computations (-28.6% saved)

regimes28.0ms (0.3%)

Memory

-26.2MiB live, 48.3MiB allocated

Counts

75 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.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 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 th))

Outputs

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

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
82.6%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes28.0ms (0.3%)

Memory

-7.5MiB live, 41.8MiB allocated

Counts

72 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sqrt (sin ky)) 4) (.f64 ky ky))))) (sin.f64 th))

Outputs

(*.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) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))

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

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
82.5%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes202.0ms (1.9%)

Memory

18.5MiB live, 244.2MiB allocated

Counts

69 → 3

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (sin.f64 th))
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 kx)) #s(literal 2 binary64)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 th) #s(literal -1 binary64))))

Outputs

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

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

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

Calls

9 calls:

36.0ms	(sin.f64 ky)
24.0ms	ky
22.0ms	th
21.0ms	(sin.f64 th)
20.0ms	kx

Results

Accuracy	Segments	Branch
50.7%	3	`(sin.f64 th)`
50.1%	2	`th`
57.5%	3	`ky`
63.3%	3	`(sin.f64 kx)`
62.9%	3	`(sin.f64 ky)`
55.9%	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))`
63.3%	2	`kx`
63.3%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
75.1%	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 42 to 51 computations (-21.4% saved)

regimes57.0ms (0.5%)

Memory

11.1MiB live, 96.2MiB 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) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(approx (+ ( 1/120 (* kx kx)) -1/6) (.f64 #s(literal 1/120 binary64) (.f64 kx kx))) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (.f64 #s(literal 1/120 binary64) kx) kx #s(literal -1/6 binary64)) kx)))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (*.f64 (/.f64 ky kx) #s(literal 1/2 binary64))) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (sin kx) (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) (pow.f64 kx #s(literal 3 binary64)) kx))) (.f64 (sin.f64 ky) (sin.f64 th))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (fma.f64 #s(approx ( (/ 1/2 (sin kx)) ky) (/.f64 (.f64 ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1/2 binary64))) kx)) ky (sin.f64 kx)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) #s(approx (sin kx) (fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (.f64 kx kx) #s(literal -1/6 binary64)) kx)))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (/.f64 (.f64 kx (fma.f64 (.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64))) ky)) kx (sin.f64 ky))) (sin.f64 ky)))
(.f64 (sin.f64 kx) (.f64 (pow.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) #s(literal -1 binary64)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 th (hypot.f64 (sin.f64 kx) (sin.f64 kx))) (sin.f64 kx)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (*.f64 (/.f64 (sin.f64 kx) (hypot.f64 (sin.f64 kx) (sin.f64 kx))) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (/.f64 (*.f64 (sin.f64 kx) th) (hypot.f64 (sin.f64 kx) (sin.f64 kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (/.f64 #s(literal 1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 kx)))))

Outputs

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

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

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

Calls

3 calls:

19.0ms	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	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
51.0%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
51.0%	2	`kx`
63.5%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 18 to 20 computations (-11.1% saved)

regimes46.0ms (0.4%)

Memory

2.0MiB live, 75.9MiB allocated

Counts

46 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (.f64 (neg.f64 (sin.f64 kx)) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 kx))) (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)) (*.f64 (sin.f64 kx) (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 (sqrt (sin ky)) 4)))) (fma.f64 (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))))))

Outputs

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

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

Calls

3 calls:

16.0ms	(sin.f64 ky)
14.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
13.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
52.2%	2	`(sin.f64 ky)`
55.8%	3	`(sin.f64 kx)`
57.3%	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 17 to 19 computations (-11.8% saved)

regimes15.0ms (0.1%)

Memory

-12.4MiB live, 23.6MiB allocated

Counts

36 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx))) (sin.f64 kx))
(/.f64 (*.f64 (sin.f64 kx) (sin.f64 th)) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sin.f64 kx)))

Outputs

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

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

Calls

1 calls:

13.0ms

(/.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
57.2%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes11.0ms (0.1%)

Memory

21.3MiB live, 21.3MiB allocated

Counts

32 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) #s(approx (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2)))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
(/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (/ 1 (pow (sin kx) -1)) (/ 1 (pow (sin kx) -1))))) (sin ky)) (/.f64 (sin.f64 kx) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 th (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (.f64 (/.f64 kx ky) kx) #s(literal 1/2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) (sin.f64 th))
(/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(approx (+ (* (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 kx kx) ky)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (.f64 (-.f64 (.f64 th th) (.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64))))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 th (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))) (-.f64 (.f64 th th) (*.f64 #s(literal 1/36 binary64) (pow.f64 th #s(literal 6 binary64))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) (neg.f64 th)) (fma.f64 (pow.f64 th #s(literal 6 binary64)) #s(literal 1/36 binary64) (*.f64 (neg.f64 th) th))))))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (*.f64 ky ky) #s(literal 1/12 binary64) #s(literal 1/2 binary64)))) ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (.f64 (/.f64 (.f64 kx kx) ky) #s(literal 1/2 binary64))))) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (+ ( (* 1/2 kx) (/ kx (sin ky))) (sin ky)) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) kx) kx (.f64 (fma.f64 (.f64 (fma.f64 (.f64 kx kx) #s(literal 7/720 binary64) #s(literal -1/6 binary64)) ky) ky (fma.f64 #s(literal 1/12 binary64) (.f64 kx kx) #s(literal 1 binary64))) (.f64 ky ky))) ky)))) (sin.f64 th))

Outputs

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

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

Calls

1 calls:

9.0ms

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

Results

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes14.0ms (0.1%)

Memory

-26.1MiB live, 13.6MiB allocated

Counts

18 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

6.0ms

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

Results

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes49.0ms (0.5%)

Memory

44.4MiB live, 118.8MiB 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) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 th th) (.f64 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) (fma.f64 (.f64 (.f64 #s(literal -1/6 binary64) th) th) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) th) #s(literal -1/6 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)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (fma.f64 (*.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)) th)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) (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)) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 binary64))) #s(literal -1/6 binary64) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3/2 binary64)) (*.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal -1/6 binary64)) th)))

Outputs

#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (*.f64 (/.f64 th (sin.f64 kx)) ky)))

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

Calls

9 calls:

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

Results

Accuracy	Segments	Branch
31.4%	1	`(sin.f64 th)`
31.4%	1	`th`
38.1%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
38.1%	2	`kx`
39.7%	2	`(sin.f64 ky)`
38.1%	3	`(sin.f64 kx)`
39.2%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
39.7%	2	`ky`
42.3%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes11.0ms (0.1%)

Memory

-18.0MiB live, 21.3MiB allocated

Counts

7 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

4.0ms	(/.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)))))
3.0ms	ky
3.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
36.8%	2	`(sin.f64 ky)`
36.5%	2	`ky`
39.2%	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 18 computations (-12.5% saved)

regimes23.0ms (0.2%)

Memory

-15.9MiB live, 36.7MiB allocated

Counts

5 → 1

Calls

Call 1

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

Calls

7 calls:

8.0ms	(*.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))
3.0ms	(sin.f64 kx)
2.0ms	(/.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	(sin.f64 ky)
2.0ms	ky

Results

Accuracy	Segments	Branch
31.4%	1	`ky`
31.4%	1	`(sin.f64 kx)`
31.4%	1	`(sin.f64 ky)`
31.4%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
31.4%	1	`kx`
31.4%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
31.4%	1	`(/.f64 (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 39 to 44 computations (-12.8% saved)

regimes22.0ms (0.2%)

Memory

0.9MiB live, 39.0MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

9 calls:

4.0ms	(sin.f64 th)
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))
2.0ms	(/.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	th
2.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
16.6%	1	`(sin.f64 ky)`
16.6%	1	`(sin.f64 kx)`
16.6%	1	`th`
16.6%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
16.6%	1	`(sin.f64 th)`
16.6%	1	`ky`
16.6%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
16.6%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
16.6%	1	`kx`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch15.0ms (0.1%)

Memory

22.0MiB live, 22.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.001159330580328828	0.003421100748027279

Samples

10.0ms

80×

valid

Compiler

Compiled 244 to 198 computations (18.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sin: 4.0ms (53.9% of total)

ival-mult: 1.0ms (13.5% of total)

ival-sqrt: 1.0ms (13.5% of total)

ival-pow2: 1.0ms (13.5% of total)

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

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

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

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

bsearch2.0ms (0%)

Memory

-35.8MiB live, 2.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.7882243690021343e-7	1.3440467923312192e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.1086928221305524e-12	2.156655347281281e-12

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.99490293846028	0.9999535926362921
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9686479439947825	0.99490293846028
0.0ms	-1.0	-0.9999996236926956

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.9686479439947825	0.99490293846028
0.0ms	-0.999959113933461	-0.987023335424855

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.02663687404445355	0.03467202939245387
0.0ms	-0.7115750769221064	-0.7004193246046863

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02663687404445355	0.03467202939245387

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.02663687404445355	0.03467202939245387

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.03361415876508e-7	0.02663687404445355

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.03361415876508e-7	0.02663687404445355

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

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

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch17.0ms (0.2%)

Memory

22.1MiB live, 22.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	6.132924771915714e-110	4.3338791018947716e-98

Samples

9.0ms

160×

valid

Compiler

Compiled 129 to 189 computations (-46.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-sin: 4.0ms (75.5% of total)

ival-mult: 1.0ms (18.9% of total)

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

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

simplify32.0ms (0.3%)

Memory

-27.0MiB live, 52.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	180	1148
1	207	1148
2	213	1148
3	217	1148
4	219	1148

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 kx #s(literal 662929865148937/288230376151711744 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 4722366482869645/9444732965739290427392 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 5323142168927135/2475880078570760549798248448 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky))) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.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)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.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)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (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))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 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 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (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 -4458563631096791/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (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 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (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)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (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 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 1080863910568919/36028797018963968 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 6338253001141147/1267650600228229401496703205376 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (.f64 (/.f64 th (sin.f64 kx)) ky))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(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 17796316275227/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th 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 kx #s(literal 662929865148937/288230376151711744 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64))) (sin.f64 th)))
(if (<=.f64 kx #s(literal 662929865148937/288230376151711744 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) kx))) #s(literal 2 binary64)))) #s(literal 2 binary64))) (sin.f64 th)))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 4722366482869645/9444732965739290427392 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx)))) (sin.f64 ky))) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)))
(if (<=.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 5323142168927135/2475880078570760549798248448 binary64)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (/.f64 #s(literal 1 binary64) #s(approx (pow (sin kx) -1) (/.f64 #s(literal 1 binary64) kx)))) (sin.f64 ky))) (*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -1 binary64)) (.f64 (/.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)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))) (sin.f64 ky)))))
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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 -1 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th)) (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 2206763817411543/2251799813685248 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (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 -4458563631096791/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (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 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 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 -4458563631096791/4503599627370496 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (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 2206763817411543/2251799813685248 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4))) (sqrt.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) (sin.f64 th)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 #s(approx (* (/ 1/2 (sin ky)) kx) (*.f64 (/.f64 kx ky) #s(literal 1/2 binary64))) kx (sin.f64 ky))) (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)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (.f64 (sin.f64 ky) th) (sqrt.f64 #s(approx (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (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 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -799388933858263/1125899906842624 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) (.f64 (sqrt.f64 #s(approx (/ 1 (+ ( (sin kx) (sin kx)) (pow (sin ky) 2))) (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 th (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 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 1080863910568919/36028797018963968 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (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 1080863910568919/36028797018963968 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 1080863910568919/36028797018963968 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (/.f64 (sin.f64 th) #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4722366482869645/4722366482869645213696 binary64)) (.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
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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 6338253001141147/1267650600228229401496703205376 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sqrt (sin ky)) 4)))) (sin th)) #s(approx (* (* (sin ky) th) (sqrt (/ 1 (+ (* (sin kx) (sin kx)) (pow (sin ky) 2))))) (.f64 (/.f64 th (sin.f64 kx)) ky))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(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 17796316275227/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 (pow.f64 th #s(literal 3 binary64)) #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 17796316275227/2404907604760405225358828131112281116032698930082119547604265954848982041717359046106827774346003151904701415424 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) #s(approx (+ (* (pow th 3) -1/6) th) (.f64 #s(literal -1/6 binary64) (pow.f64 th #s(literal 3 binary64)))))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (.f64 (.f64 th th) #s(literal -1/6 binary64)) th th)))

soundness1.6s (15.6%)

Memory

32.4MiB live, 931.7MiB allocated

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	425	10037
1	1364	9781
2	5255	9480
0	8366	8927
0	50	285
0	81	223
1	266	219
2	1409	215
0	9126	215
0	13	49
0	22	49
1	62	49
2	338	49
3	2902	49
0	8284	34
0	554	10648
1	1822	10338
2	7378	10294
0	8052	9624
0	466	10008
1	1476	9664
2	5509	9307
0	8160	8620

Stop Event

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

Compiler

Compiled 1 727 to 836 computations (51.6% saved)

preprocess267.0ms (2.5%)

Memory

0.0MiB live, 249.4MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 1 578 to 484 computations (69.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	50	346
0	81	341
1	115	341
2	153	341
3	175	341
4	182	341
5	188	341
6	188	341
7	228	341
8	228	341
9	275	341
10	307	341
11	357	341
12	361	341
0	361	341

Iter	Nodes	Cost
0	65	495
0	105	485
1	168	434
2	279	431
3	370	431
4	398	431
5	438	431
6	438	431
7	544	431
8	570	431
9	594	431
0	594	428

Iter	Nodes	Cost
0	50	346
0	81	341
1	115	341
2	153	341
3	175	341
4	182	341
5	188	341
6	188	341
7	228	341
8	228	341
9	275	341
10	307	341
11	357	341
12	361	341
0	361	341

Iter	Nodes	Cost
0	65	495
0	105	485
1	168	434
2	279	431
3	370	431
4	398	431
5	438	431
6	438	431
7	544	431
8	570	431
9	594	431
0	594	428

start0.0ms (0%)

analyze197.0ms (1.9%)

sample2.4s (22.6%)

explain270.0ms (2.6%)

preprocess106.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize61.0ms (0.6%)

series42.0ms (0.4%)

simplify213.0ms (2%)

rewrite496.0ms (4.7%)

eval110.0ms (1%)

prune38.0ms (0.4%)

simplify119.0ms (1.1%)

localize125.0ms (1.2%)

series86.0ms (0.8%)

simplify226.0ms (2.1%)

rewrite115.0ms (1.1%)

eval326.0ms (3.1%)

prune347.0ms (3.3%)

simplify15.0ms (0.1%)

localize176.0ms (1.7%)

series72.0ms (0.7%)

simplify214.0ms (2%)

rewrite137.0ms (1.3%)

eval182.0ms (1.7%)

prune176.0ms (1.7%)

simplify23.0ms (0.2%)

localize168.0ms (1.6%)

series60.0ms (0.6%)

simplify182.0ms (1.7%)

rewrite204.0ms (1.9%)

eval135.0ms (1.3%)

prune141.0ms (1.3%)

regimes351.0ms (3.3%)

regimes219.0ms (2.1%)

regimes141.0ms (1.3%)

regimes48.0ms (0.5%)

regimes154.0ms (1.5%)

regimes28.0ms (0.3%)

regimes28.0ms (0.3%)

regimes202.0ms (1.9%)

regimes57.0ms (0.5%)

regimes46.0ms (0.4%)

regimes15.0ms (0.1%)

regimes11.0ms (0.1%)

regimes14.0ms (0.1%)

regimes49.0ms (0.5%)

regimes11.0ms (0.1%)

regimes23.0ms (0.2%)

regimes22.0ms (0.2%)

bsearch15.0ms (0.1%)

bsearch2.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch17.0ms (0.2%)

simplify32.0ms (0.3%)

soundness1.6s (15.6%)

preprocess267.0ms (2.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	50	346
0	81	341
1	115	341
2	153	341
3	175	341
4	182	341
5	188	341
6	188	341
7	228	341
8	228	341
9	275	341
10	307	341
11	357	341
12	361	341
0	361	341

Iter	Nodes	Cost
0	65	495
0	105	485
1	168	434
2	279	431
3	370	431
4	398	431
5	438	431
6	438	431
7	544	431
8	570	431
9	594	431
0	594	428