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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze197.0ms (1.8%)

Memory

14.0MiB live, 248.7MiB 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)

sample2.0s (19%)

Memory

-24.9MiB live, 2 542.3MiB allocated

Samples

1.6s

8 256×

valid

Precisions

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

ival-sin: 639.0ms (60.1% of total)

ival-pow2: 169.0ms (15.9% of total)

ival-sqrt: 75.0ms (7.1% of total)

ival-mult: 69.0ms (6.5% of total)

ival-div: 57.0ms (5.4% of total)

ival-add: 44.0ms (4.1% of total)

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

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

Bogosity

explain290.0ms (2.7%)

Memory

12.3MiB live, 223.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
13	-	1	(-8.207160447921242e-158 -3.754344193174343e-208 3.3978315233589894e-160)	`(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	12	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	50
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	59
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	12

Confusion

	Predicted +	Predicted -
+	12	1
-	0	243

Precision

1.0

Recall

0.9230769230769231

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	12	0	1
-	0	0	243

Precision?

1.0

Recall?

0.9230769230769231

Freqs

test

number	freq
0	244
1	12

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

78.0ms

512×

valid

Compiler

Compiled 218 to 56 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-sin: 34.0ms (59.1% of total)

ival-pow2: 10.0ms (17.4% of total)

ival-div: 3.0ms (5.2% of total)

ival-mult: 3.0ms (5.2% of total)

ival-sqrt: 3.0ms (5.2% of total)

ival-add: 2.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess130.0ms (1.2%)

Memory

-17.6MiB live, 61.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.0%	(*.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))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify3.0ms (0%)

Memory

3.6MiB live, 3.6MiB 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 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(sin.f64 ky)
ky
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(sin.f64 kx)
kx
#s(literal 2 binary64)
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(sin.f64 th)
th

localize111.0ms (1%)

Memory

-6.9MiB live, 64.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(*.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))
accuracy	0.22884750976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	0.23828125	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	2.98437304593146	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

63.0ms

256×

valid

Compiler

Compiled 134 to 28 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-pow2: 29.0ms (54.8% of total)

ival-sin: 17.0ms (32.1% of total)

ival-div: 2.0ms (3.8% of total)

ival-mult: 2.0ms (3.8% of total)

ival-sqrt: 2.0ms (3.8% of total)

ival-add: 1.0ms (1.9% of total)

exact: 1.0ms (1.9% of total)

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

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

series63.0ms (0.6%)

Memory

1.3MiB live, 39.0MiB allocated

Counts

6 → 120

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
(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)
(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)
(* (* 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)))))

Calls

9 calls:

Time	Variable		Point	Expression
38.0ms	th	@	-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))
6.0ms	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))
3.0ms	kx	@	-inf	((sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (pow (sin kx) 2) (pow (sin ky) 2))

simplify244.0ms (2.3%)

Memory

22.7MiB live, 173.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	317	2263
1	1011	2214
2	3847	2122
3	7794	2122
0	8097	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)
(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)
(* (* 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)))))

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

rewrite220.0ms (2.1%)

Memory

-0.8MiB live, 203.2MiB 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
(*.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))) (-.f64 (pow.f64 (sin.f64 kx) #s(literal 6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))))
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(/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 ky) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1/8 binary64) (pow.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 3 binary64)))) (+.f64 #s(literal 1/4 binary64) (+.f64 (pow.f64 (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))) #s(literal -2 binary64))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64)))) #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 ky #s(literal 2 binary64))))))
(-.f64 #s(literal 1/2 binary64) (/.f64 (cos.f64 (*.f64 ky #s(literal 2 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (sin.f64 ky))) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 (sin.f64 ky))))
(exp.f64 (log.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 ky #s(literal 2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 (.f64 (cos.f64 (.f64 ky #s(literal 2 binary64))) #s(literal 1/2 binary64))))

eval97.0ms (0.9%)

Memory: 23.0MiB live, 130.9MiB allocated
Compiler: Compiled 11 434 to 1 725 computations (84.9% saved)

prune118.0ms (1.1%)

Memory

-24.4MiB live, 99.0MiB allocated

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	425	23	448
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	426	23	449

Accuracy

100.0%

Counts

449 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (pow.f64 (sin.f64 ky) #s(literal -1 binary64)))
▶	97.2%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
▶	98.8%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	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))
	78.6%	(.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))
	90.3%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
▶	45.7%	(.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))
	86.8%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	87.0%	(.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 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	54.5%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	35.7%	(.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
	30.9%	(.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))
	33.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	99.7%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (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))
	68.6%	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	99.4%	(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	22.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
	29.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	93.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky))))
▶	27.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 866 to 684 computations (21% saved)

simplify8.0ms (0.1%)

Memory

18.9MiB live, 18.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
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	(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(sin.f64 th)
cost-diff	0	(*.f64 (sin.f64 th) (sin.f64 ky))
cost-diff	0	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff	0	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
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)) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))))
cost-diff	0	(.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))
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	33	221
0	54	214
1	70	214
2	82	214
3	101	214
4	150	214
5	162	214
6	172	214
0	172	214

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

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

localize154.0ms (1.4%)

Memory

-0.0MiB live, 118.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.15234375	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
accuracy	0.21484375	(/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th))
accuracy	0.6627557937882699	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
accuracy	0	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.17578125	(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy	1.8336662135701942	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.1484375	(.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))
accuracy	0.23828125	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	2.98437304593146	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))
accuracy	32.243952665690436	#s(approx (pow (sin ky) 2) (*.f64 ky ky))
accuracy	0	(sin.f64 th)
accuracy	46.21252500905018	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.1484375	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.1484375	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Samples

118.0ms

256×

valid

Compiler

Compiled 484 to 59 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-sin: 73.0ms (73.9% of total)

ival-div: 8.0ms (8.1% of total)

ival-mult: 6.0ms (6.1% of total)

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

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

ival-sqrt: 2.0ms (2% of total)

ival-add: 1.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series49.0ms (0.5%)

Memory

12.0MiB live, 49.9MiB allocated

Counts

17 → 420

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

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

Calls

9 calls:

Time	Variable		Point	Expression
19.0ms	kx	@	-inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (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)) (sin kx) (pow (sin ky) 2) (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))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (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)) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (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)) (sin kx) (pow (sin ky) 2) (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))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (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)) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2))
3.0ms	th	@	-inf	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (* (sin th) (sin ky)) (/ 1 (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (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)) (sin kx) (pow (sin ky) 2) (pow (sin kx) 2))

simplify212.0ms (2%)

Memory

-6.2MiB live, 188.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	518	9344
1	1671	8918
2	6197	8588
0	8691	7946

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 417

Calls

Call 1

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

Outputs
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (sin.f64 th))))) (.f64 kx kx) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (+.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (/.f64 (+.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal -1/6 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
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(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
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#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
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(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (sin.f64 ky)) kx) kx (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
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(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))
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(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
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(/.f64 #s(literal 1 binary64) (sin.f64 th))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(fma.f64 (fma.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 th)) (.f64 kx (/.f64 kx (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) (/.f64 #s(literal 1 binary64) (sin.f64 th)))
(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 (/.f64 kx (sin.f64 th)) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.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 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 th)) (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (sin.f64 th))))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #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 kx) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (.f64 (-.f64 #s(literal 2/45 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/6 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))
kx
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) #s(literal -1/6 binary64) kx)
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 #s(literal 1/120 binary64) (*.f64 kx kx) #s(literal -1/6 binary64)) kx)
(fma.f64 (pow.f64 kx #s(literal 3 binary64)) (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 kx kx) #s(literal 1/120 binary64)) (.f64 kx kx) #s(literal -1/6 binary64)) kx)
(*.f64 kx kx)
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) #s(literal -1/3 binary64) (*.f64 kx kx))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 #s(literal 2/45 binary64) (.f64 kx kx) #s(literal -1/3 binary64)) (.f64 kx kx))
(fma.f64 (pow.f64 kx #s(literal 4 binary64)) (fma.f64 (fma.f64 #s(literal -1/315 binary64) (.f64 kx kx) #s(literal 2/45 binary64)) (.f64 kx kx) #s(literal -1/3 binary64)) (*.f64 kx kx))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
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(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))
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(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
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(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 ky) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)))
(.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))))) (.f64 (.f64 (sin.f64 ky) (fma.f64 (.f64 th th) #s(literal 1/120 binary64) #s(literal -1/6 binary64))) (.f64 th th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 ky))) th)
(.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal -1/6 binary64) #s(literal 1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (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))))) (.f64 (sin.f64 ky) (fma.f64 (*.f64 th th) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))))) th)
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))
(/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)
(/.f64 (fma.f64 (.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (fma.f64 (.f64 th th) #s(literal 7/360 binary64) #s(literal 1/6 binary64))) (*.f64 th th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)
(/.f64 (fma.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (.f64 (pow.f64 th #s(literal 4 binary64)) (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 (.f64 th (/.f64 th (sin.f64 ky))) #s(literal 31/15120 binary64) (/.f64 #s(literal 7/360 binary64) (sin.f64 ky)))))) th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(*.f64 (sin.f64 th) (sin.f64 ky))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th)) (sin.f64 ky))

rewrite347.0ms (3.2%)

Memory

-13.6MiB live, 199.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	160
0	54	153
1	183	153
2	1099	153
0	8204	153

Stop Event

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

Counts

17 → 806

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

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

eval375.0ms (3.5%)

Memory: 5.9MiB live, 385.5MiB allocated
Compiler: Compiled 39 881 to 2 848 computations (92.9% saved)

prune97.0ms (0.9%)

Memory

-9.4MiB live, 146.7MiB allocated

Pruning

39 alts after pruning (37 fresh and 2 done)

	Pruned	Kept	Total
New	1 536	25	1 561
Fresh	6	12	18
Picked	3	2	5
Done	0	0	0
Total	1 545	39	1 584

Accuracy

100.0%

Counts

1 584 → 39

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))
✓	97.2%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	78.5%	(/.f64 (.f64 (sin.f64 th) (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 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
	35.5%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
	31.3%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
	99.6%	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	45.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
	46.5%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	49.8%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	96.6%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	78.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky)) (sin.f64 th)))
	32.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
	30.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) ky) ky (sin.f64 kx)) ky)) (sin.f64 th)))
	29.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
	27.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th)))
	98.7%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))))
	49.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
	52.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
▶	99.6%	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
	78.6%	(.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))
	90.3%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	87.0%	(.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 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	37.7%	(.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))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	19.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
▶	54.5%	(.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))
	29.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	30.9%	(.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))
	33.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶	99.7%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (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))
	45.7%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
	45.6%	(.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 th)))
	22.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin 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))) (sin.f64 th))
▶	22.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
	29.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
✓	27.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	15.4%	#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)))
▶	15.4%	#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 1 702 to 1 268 computations (25.5% saved)

simplify16.0ms (0.2%)

Memory

-24.6MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
cost-diff	0	(sin.f64 th)
cost-diff	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
cost-diff	0	(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
cost-diff	0	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	0	(*.f64 #s(literal -1/2 binary64) kx)
cost-diff	0	(fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
cost-diff	0	#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)))
cost-diff	0	(.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))
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	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	300
0	70	287
1	102	283
2	139	281
3	222	281
4	311	281
5	354	281
6	354	281
7	375	281
8	375	281
0	375	281

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize114.0ms (1.1%)

Memory

38.1MiB live, 228.6MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.21484375	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.21875	(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))
accuracy	0.1484375	(.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))
accuracy	0.22884750976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	2.98437304593146	(sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (*.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	31.630261329344812	#s(approx (pow (sin kx) 2) (*.f64 kx kx))
accuracy	0.22884750976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	1.0151076747369494	(fma.f64 (*.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))
accuracy	4.111543235009687	(/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))
accuracy	48.44953256597601	#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)))
accuracy	0	(pow.f64 th #s(literal 3 binary64))
accuracy	0.05859375	(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
accuracy	30.890108364798625	#s(approx (sin th) (fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th))
accuracy	46.21252500905018	#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	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.1484375	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
accuracy	0.15234375	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Samples

88.0ms

256×

valid

Compiler

Compiled 592 to 76 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-sin: 19.0ms (28.3% of total)

ival-div: 13.0ms (19.4% of total)

ival-mult: 11.0ms (16.4% of total)

ival-pow2: 6.0ms (8.9% of total)

ival-add: 5.0ms (7.5% of total)

ival-hypot: 4.0ms (6% of total)

const: 4.0ms (6% of total)

ival-pow: 3.0ms (4.5% of total)

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

exact: 1.0ms (1.5% of total)

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

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

series99.0ms (0.9%)

Memory

-16.3MiB live, 97.5MiB allocated

Counts

23 → 516

Calls

Call 1

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

Outputs
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
(+ 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))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(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 ky))
(+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* 1/2 (* (pow kx 2) (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))) (/ (sin th) (sin ky)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 3))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (sin ky) (* (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 (* (sin ky) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))) (/ (sin th) (sin ky)))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (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))))
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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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 (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)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(sin kx)
(sin kx)
(sin kx)
(sin kx)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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 (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)))))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(* -1/2 kx)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(sin kx)
(sin kx)
(sin kx)
(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))))
(/ (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))))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(/ ky (sin kx))
(* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* 1/12 (/ 1 (pow (sin kx) 3)))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
(* ky (+ (* (pow ky 2) (- (* (pow ky 2) (+ (* 1/120 (/ 1 (sin kx))) (+ (* 1/12 (/ 1 (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))) (* (pow ky 2) (- (+ (* -1/2 (* (sin kx) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8))))))) (* -1/12 (* (sin kx) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* 1/5040 (/ 1 (sin kx))) (* 1/240 (/ 1 (pow (sin kx) 3)))))))))) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))
ky
(* ky (+ 1 (* -1/6 (pow ky 2))))
(* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))
(* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))
(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 th) (sin kx))
(+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (pow ky 2) (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))))))))) (/ (sin th) (sin kx)))
(+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* (pow ky 2) (+ (* -1/2 (* (pow ky 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))))))))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))) (/ (sin th) (sin kx)))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 kx) (+ (* 2/135 kx) (* 1/3 (+ (* -1/9 kx) (* 2/45 kx))))))) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(pow 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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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 (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)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(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 th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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 (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)))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin ky)
(sin ky)
(sin ky)
(sin ky)
(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 th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(pow (sin ky) 2)
(pow (sin ky) 2)
(pow (sin ky) 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 (* (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 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* -1/6 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/120 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))))))))
(* th (+ (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* -1/6 (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* 1/120 (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))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)
(* -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)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(sin th)
(sin th)
(sin th)
(sin th)

Calls

9 calls:

Time	Variable		Point	Expression
44.0ms	ky	@	-inf	((/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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 (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (* -1/2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (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 th) (/ kx (pow (sin ky) 2)) (pow (sin ky) 2) (pow (sin kx) 2) (sin kx))
22.0ms	kx	@	0	((/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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 (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (* -1/2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (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 th) (/ kx (pow (sin ky) 2)) (pow (sin ky) 2) (pow (sin kx) 2) (sin kx))
6.0ms	th	@	-inf	((/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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 (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (* -1/2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (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 th) (/ kx (pow (sin ky) 2)) (pow (sin ky) 2) (pow (sin kx) 2) (sin kx))
4.0ms	kx	@	inf	((/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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 (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (* -1/2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (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 th) (/ kx (pow (sin ky) 2)) (pow (sin ky) 2) (pow (sin kx) 2) (sin kx))
4.0ms	ky	@	inf	((/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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 (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (* -1/2 kx) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (/ (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 th) (/ kx (pow (sin ky) 2)) (pow (sin ky) 2) (pow (sin kx) 2) (sin kx))

simplify247.0ms (2.3%)

Memory

-6.3MiB live, 310.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	529	10392
1	1693	10038
2	6497	9737
0	8053	9172

Stop Event

1×	iter limit
1×	node limit

Counts

516 → 511

Calls

Call 1

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

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

rewrite172.0ms (1.6%)

Memory

12.8MiB live, 327.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	241
0	70	222
1	239	222
2	1425	222
0	8253	222

Stop Event

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

Counts

23 → 580

Calls

Call 1

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

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

eval267.0ms (2.5%)

Memory: 16.6MiB live, 491.5MiB allocated
Compiler: Compiled 42 595 to 3 288 computations (92.3% saved)

prune136.0ms (1.3%)

Memory

4.0MiB live, 211.6MiB allocated

Pruning

56 alts after pruning (53 fresh and 3 done)

	Pruned	Kept	Total
New	1 404	28	1 432
Fresh	7	25	32
Picked	4	1	5
Done	0	2	2
Total	1 415	56	1 471

Accuracy

100.0%

Counts

1 471 → 56

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))
✓	97.2%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	78.5%	(/.f64 (.f64 (sin.f64 th) (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 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
	31.3%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
	45.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
	46.5%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	49.8%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	96.6%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	78.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky)) (sin.f64 th)))
	32.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
▶	53.1%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
	29.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
	27.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th)))
	98.7%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))))
	49.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
	52.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
	78.5%	(.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))
	30.9%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
	27.8%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
	33.0%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
	78.6%	(.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))
	87.0%	(.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 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	37.7%	(.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))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	19.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
✓	54.5%	(.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))
	46.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	29.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	33.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	99.4%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) (sin.f64 ky))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))) (sin.f64 th))
▶	33.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	33.0%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
	29.7%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (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))
	45.7%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
	54.3%	(.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))) #s(literal -1/2 binary64)) (sin.f64 th)))
	14.0%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	23.5%	(.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 #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
	22.9%	(.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 #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
▶	11.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
	12.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
	18.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
	29.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	14.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
	15.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
	3.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
✓	27.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	15.4%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 binary64)) #s(literal -1/6 binary64) th)))
	15.4%	#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)))
	15.4%	#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)))
	15.4%	#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)))
▶	15.4%	#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)))
	15.4%	#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)))
	12.6%	#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)))))
	6.5%	#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 2 978 to 2 108 computations (29.2% saved)

simplify128.0ms (1.2%)

Memory

3.8MiB live, 119.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
cost-diff	0	(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
cost-diff	0	(/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky)))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
cost-diff	0	#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))
cost-diff	0	(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
cost-diff	704	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
cost-diff	0	#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64)))
cost-diff	0	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
cost-diff	320	(fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (*.f64 #s(literal 1/3 binary64) kx))
cost-diff	448	(fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (*.f64 #s(literal 1/15 binary64) kx))
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	(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)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	551
0	108	536
1	178	532
2	319	505
3	779	505
4	1993	498
5	3380	498
6	5706	498
0	8112	480

Stop Event

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

Calls

Call 1

Inputs
(.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
#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 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64)))
(fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) kx)
#s(literal -1/2 binary64)
kx
#s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky)))
(/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))
(fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx)
(fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (*.f64 #s(literal 1/3 binary64) kx))
(fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (*.f64 #s(literal 1/15 binary64) kx))
(neg.f64 ky)
ky
(.f64 ky (.f64 kx #s(literal -2/189 binary64)))
(*.f64 kx #s(literal -2/189 binary64))
#s(literal -2/189 binary64)
(*.f64 #s(literal 1/15 binary64) kx)
#s(literal 1/15 binary64)
(*.f64 ky ky)
(*.f64 #s(literal 1/3 binary64) kx)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
(sin.f64 th)
th
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
#s(literal 1 binary64)
(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))
(sin.f64 kx)
kx
(sin.f64 ky)
ky
(sin.f64 th)
th
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
(sin.f64 ky)
ky
#s(approx (pow (sin kx) 2) (*.f64 kx kx))
(*.f64 kx kx)
kx
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
th

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

localize439.0ms (4.1%)

Memory

-7.1MiB live, 319.4MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.6627557937882699	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
accuracy	1.6972883925684794	(/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky)))
accuracy	2.98437304593146	(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
accuracy	31.630261329344812	#s(approx (pow (sin kx) 2) (*.f64 kx kx))
accuracy	0.1484375	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
accuracy	0.15234375	(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))
accuracy	0.17578125	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
accuracy	45.03305549502388	#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))
accuracy	1.0151076747369494	(fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64))
accuracy	19.125741849612286	(/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))
accuracy	32.05718198408464	#s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky)))
accuracy	48.44953256597601	#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64)))
accuracy	0.03515625	(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)
accuracy	0.19140625	(.f64 #s(literal -1/6 binary64) (.f64 th th))
accuracy	30.890108364798625	#s(approx (sin th) (fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th))
accuracy	46.21252500905018	#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	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.1484375	(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky))) (sin.f64 th))
accuracy	0.1953125	(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	0.328125	(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (neg.f64 (sin.f64 ky)))

Samples

351.0ms

256×

valid

Compiler

Compiled 1 014 to 121 computations (88.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 305.0ms

ival-pow2: 141.0ms (46.3% of total)

ival-mult: 73.0ms (24% of total)

const: 39.0ms (12.8% of total)

ival-sin: 18.0ms (5.9% of total)

ival-div: 15.0ms (4.9% of total)

ival-add: 9.0ms (3% of total)

ival-hypot: 4.0ms (1.3% of total)

ival-sqrt: 4.0ms (1.3% of total)

ival-neg: 2.0ms (0.7% of total)

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

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

exact: 0.0ms (0% of total)

series59.0ms (0.5%)

Memory

-24.0MiB live, 129.5MiB allocated

Counts

25 → 612

Calls

Call 1

Inputs
(*.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)))
(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 (.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)
(fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (*.f64 #s(literal 1/15 binary64) kx))
(fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (*.f64 #s(literal 1/3 binary64) kx))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)
#s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky)))
(/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))
(fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))

Outputs
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 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))))))))))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (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
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ 1 (sin th))
(+ (* 1/2 (/ (pow kx 2) (* (pow (sin ky) 2) (sin th)))) (/ 1 (sin th)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th)))
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (pow (sin ky) 2) (sin th)))) (* 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) (sin th)))))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(pow kx 2)
(* (pow 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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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)))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
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(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
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(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
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(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(pow (sin kx) 2)
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(pow (sin kx) 2)
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(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
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(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
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(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(/ 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)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* 1/15 kx)
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(* 1/3 kx)
(+ (* 1/15 (* kx (pow ky 2))) (* 1/3 kx))
(+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))))
(+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 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 (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))))
(/ (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))))
(/ (sin kx) (* ky (sin th)))
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) ky)
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (* 1/12 (/ 1 (* (sin kx) (sin th)))))))))) (/ (sin kx) (sin th))) ky)
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (+ (* 1/12 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 31/15120 (/ (sin kx) (sin th))) (+ (* 7/720 (/ 1 (* (sin kx) (sin th)))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (* (sin kx) (sin th))))))))))))))) (/ (sin kx) (sin th))) 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))))))
(pow (sin kx) 2)
(+ (pow ky 2) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) (pow (sin kx) 2))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 kx) (+ (* 2/135 kx) (* 1/3 (+ (* -1/9 kx) (* 2/45 kx))))))) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (+ (* 1/15 (* kx (pow ky 2))) (* 1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx)))))) (pow ky 2))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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)))))
(* 2/189 (* kx (pow ky 2)))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* 2/189 (* kx (pow ky 4)))
(* (pow ky 4) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 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)))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (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)))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* 2/189 (* kx (pow ky 4)))
(* (pow ky 4) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (+ (* 1/3 (/ kx (pow ky 4))) (/ kx (pow ky 6))))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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)))))
(* 2/189 (* kx (pow ky 2)))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* 2/189 (* kx (pow ky 4)))
(* (pow ky 4) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 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)))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (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)))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* 2/189 (* kx (pow ky 4)))
(* (pow ky 4) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (* 1/3 (/ kx (pow ky 4))))))
(* (pow ky 4) (+ (* 2/189 kx) (+ (* 1/15 (/ kx (pow ky 2))) (+ (* 1/3 (/ kx (pow ky 4))) (/ kx (pow ky 6))))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(* (* 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))))
(* -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))))))))))))
(* (/ 1 (* th (sin ky))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(/ (+ (* 1/6 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) th)
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 7/360 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))) th)
(/ (+ (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (* (pow th 2) (+ (* 1/6 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* (pow th 2) (+ (* 31/15120 (* (/ (pow th 2) (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))) (* 7/360 (* (/ 1 (sin ky)) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))) th)
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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (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 ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 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 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (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)))))

Calls

9 calls:

Time	Variable		Point	Expression
11.0ms	kx	@	-inf	((* (/ -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))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th th) (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky)))) (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky))) (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (+ (* (* -1/6 (* th th)) th) th) (/ kx (pow (sin ky) 2)) (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (pow (sin kx) 2))
8.0ms	kx	@	0	((* (/ -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))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th th) (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky)))) (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky))) (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (+ (* (* -1/6 (* th th)) th) th) (/ kx (pow (sin ky) 2)) (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (pow (sin kx) 2))
6.0ms	ky	@	-inf	((* (/ -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))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th th) (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky)))) (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky))) (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (+ (* (* -1/6 (* th th)) th) th) (/ kx (pow (sin ky) 2)) (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (pow (sin kx) 2))
6.0ms	kx	@	inf	((* (/ -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))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th th) (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky)))) (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky))) (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (+ (* (* -1/6 (* th th)) th) th) (/ kx (pow (sin ky) 2)) (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (pow (sin kx) 2))
5.0ms	ky	@	inf	((* (/ -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))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* -1/6 (* th th)) (* th th) (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky))) (* (/ 1 (/ (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)))) (/ 1 (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky)))) (/ (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (* (sin th) (sin ky))) (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (+ (* (* -1/6 (* th th)) th) th) (/ kx (pow (sin ky) 2)) (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (+ (* (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (pow (sin kx) 2))

simplify276.0ms (2.6%)

Memory

16.3MiB live, 340.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	624	12516
1	1984	12113
2	7537	12113
0	8295	11156

Stop Event

1×	iter limit
1×	node limit

Counts

612 → 610

Calls

Call 1

Inputs
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 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))))))))))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (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
(+ 1 (* 1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (pow (sin ky) 2))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(+ 1 (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (pow (sin ky) 2))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(sin th)
(+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))))))
(+ (sin th) (* (pow kx 2) (+ (* -1/2 (/ (sin th) (pow (sin ky) 2))) (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8))))))))) (* 1/2 (* (pow (sin ky) 2) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))))))))
(/ 1 (sin th))
(+ (* 1/2 (/ (pow kx 2) (* (pow (sin ky) 2) (sin th)))) (/ 1 (sin th)))
(+ (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (* (pow (sin ky) 2) (sin th)))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th)))
(+ (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (* (pow (sin ky) 2) (sin th)))) (* 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) (sin th)))))) (* 1/2 (/ 1 (* (pow (sin ky) 2) (sin th)))))) (/ 1 (sin th)))
(sin ky)
(+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))
(+ (sin ky) (* (pow kx 2) (+ (* -1/2 (/ (* (pow kx 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2))))) (sin ky))) (* 1/2 (/ 1 (sin ky))))))
(+ (sin ky) (* (pow kx 2) (+ (* (pow kx 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (sin ky))) (* 1/2 (/ (* (pow kx 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin ky) 2)))) (pow (sin ky) 2))))) (sin ky))))) (* 1/2 (/ 1 (sin ky))))))
(pow (sin ky) 2)
(+ (pow kx 2) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2)))) (pow (sin ky) 2))
(+ (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3)))) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
1
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))
(pow kx 2)
(* (pow 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) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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)))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/15 (* 2/189 (pow ky 2))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* kx (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2))))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 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)))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (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)))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(/ (* kx (+ 1 (* (pow ky 2) (+ 1/3 (* (pow ky 2) (+ 1/15 (* 2/189 (pow ky 2)))))))) (pow ky 2))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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 (* kx (- (* -2/189 (pow ky 2)) 1/15)))
(* -1 (* kx (- (* -2/189 (pow ky 2)) 1/15)))
(* -1 (* kx (- (* -2/189 (pow ky 2)) 1/15)))
(* -1 (* kx (- (* -2/189 (pow ky 2)) 1/15)))
(* -1 (* kx (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)))
(* -1 (* kx (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)))
(* -1 (* kx (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)))
(* -1 (* kx (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (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)))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (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)))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(+ (pow (sin kx) 2) (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(/ kx (pow (sin ky) 2))
(* -1 (/ (* kx (- (* (pow ky 2) (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)) 1)) (pow ky 2)))
(* -1 (/ (* kx (- (* (pow ky 2) (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)) 1)) (pow ky 2)))
(* -1 (/ (* kx (- (* (pow ky 2) (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)) 1)) (pow ky 2)))
(* -1 (/ (* kx (- (* (pow ky 2) (- (* (pow ky 2) (- (* -2/189 (pow ky 2)) 1/15)) 1/3)) 1)) (pow ky 2)))
(* -1/2 (/ (pow kx 2) (pow (sin ky) 2)))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(* (pow kx 2) (- (/ 1 (pow kx 2)) (* 1/2 (/ 1 (pow (sin ky) 2)))))
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(pow (sin kx) 2)
(/ 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)))
(sin kx)
(+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))
(+ (sin kx) (* (pow ky 2) (+ (* -1/2 (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2))))) (sin kx))) (* 1/2 (/ 1 (sin kx))))))
(+ (sin kx) (* (pow ky 2) (+ (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (sin kx))) (* 1/2 (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2))))) (sin kx))))) (* 1/2 (/ 1 (sin kx))))))
(/ (* ky (sin th)) (sin kx))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))))))))) (/ (sin th) (sin kx))))
(* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (+ (* -1/6 (/ (sin th) (sin kx))) (* (pow ky 2) (+ (* 1/120 (/ (sin th) (sin kx))) (+ (* 1/12 (/ (sin th) (pow (sin kx) 3))) (+ (* 1/2 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (* (pow ky 2) (+ (* -1/2 (* (sin kx) (* (sin th) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6)))) (pow (sin kx) 2))) (+ (* 2/45 (/ 1 (pow (sin kx) 4))) (+ (* 2/3 (/ 1 (pow (sin kx) 6))) (/ 1 (pow (sin kx) 8)))))))) (+ (* -1/12 (* (sin kx) (* (sin th) (+ (* 1/3 (/ 1 (pow (sin kx) 4))) (* 3/4 (/ 1 (pow (sin kx) 6))))))) (+ (* -1/240 (/ (sin th) (pow (sin kx) 3))) (* -1/5040 (/ (sin th) (sin kx)))))))))))))) (/ (sin th) (sin kx))))
(* 1/15 kx)
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))
(* 1/3 kx)
(+ (* 1/15 (* kx (pow ky 2))) (* 1/3 kx))
(+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx))))
(+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 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 (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))))
(/ (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))))
(/ (sin kx) (* ky (sin th)))
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (* 1/2 (/ 1 (* (sin kx) (sin th)))))) (/ (sin kx) (sin th))) ky)
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (* 1/12 (/ 1 (* (sin kx) (sin th)))))))))) (/ (sin kx) (sin th))) ky)
(/ (+ (* (pow ky 2) (+ (* 1/6 (/ (sin kx) (sin th))) (+ (* 1/2 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 7/360 (/ (sin kx) (sin th))) (+ (* 1/12 (/ 1 (* (sin kx) (sin th)))) (* (pow ky 2) (+ (* -1/12 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (* (sin kx) (sin th)))) (+ (* 31/15120 (/ (sin kx) (sin th))) (+ (* 7/720 (/ 1 (* (sin kx) (sin th)))) (* 1/2 (/ (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (pow (sin kx) 2)))) (pow (sin kx) 2)))) (* (sin kx) (sin th))))))))))))))) (/ (sin kx) (sin th))) 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))))))
(pow (sin kx) 2)
(+ (pow ky 2) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2)))) (pow (sin kx) 2))
(+ (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3)))) (pow (sin kx) 2))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (- (* (pow ky 2) (- (* -1 (* (pow ky 2) (+ (* -1/315 kx) (+ (* 2/135 kx) (* 1/3 (+ (* -1/9 kx) (* 2/45 kx))))))) (+ (* -1/9 kx) (* 2/45 kx)))) (* -1/3 kx)))) (pow ky 2))
(/ kx (pow ky 2))
(/ (+ kx (* 1/3 (* kx (pow ky 2)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (+ (* 1/15 (* kx (pow ky 2))) (* 1/3 kx)))) (pow ky 2))
(/ (+ kx (* (pow ky 2) (+ (* 1/3 kx) (* (pow ky 2) (+ (* 2/189 (* kx (pow ky 2))) (* 1/15 kx)))))) (pow ky 2))
(* -1/2 (/ (pow kx 2) (pow ky 2)))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (* -1/6 (pow kx 2))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* 1/2 (* (pow ky 2) (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2))))))))) (pow ky 2))
(/ (+ (* -1/2 (pow kx 2)) (* (pow ky 2) (+ 1 (+ (* -1/6 (pow kx 2)) (* (pow ky 2) (+ (* 1/2 (* (pow ky 2) (+ (* -1/315 (pow kx 2)) (+ (* 2/135 (pow kx 2)) (* 1/3 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))) (* 1/2 (+ (* -1/9 (pow kx 2)) (* 2/45 (pow kx 2)))))))))) (pow ky 2))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (sin ky) (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)))))
(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)))))
(* 2/189 (* kx (pow ky 2)))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
(* (pow ky 2) (+ (* 2/189 kx) (* 1/15 (/ kx (pow ky 2)))))
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th
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th
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(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))))
(* (/ 1 (* (sin ky) (sin th))) (sqrt (+ (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)))))

Outputs
#s(literal 1 binary64)
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(/.f64 #s(literal -1 binary64) (sin.f64 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)))
(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)))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 ky)) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 kx kx)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 ky)))) (.f64 kx kx) (/.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)))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (/.f64 (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))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 ky))) (.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) kx)
(.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) kx)
(.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) kx)
(.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) kx)
(.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (*.f64 ky ky) #s(literal 1/3 binary64)) kx)
(.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (*.f64 ky ky) #s(literal 1/3 binary64)) kx)
(.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (*.f64 ky ky) #s(literal 1/3 binary64)) kx)
(.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (*.f64 ky ky) #s(literal 1/3 binary64)) kx)
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(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))
#s(literal 1 binary64)
(fma.f64 (*.f64 kx (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 kx kx) #s(literal 1 binary64))
(sin.f64 th)
(fma.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (/.f64 (sin.f64 th) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (sin.f64 th))
(fma.f64 (fma.f64 (.f64 (.f64 kx kx) #s(literal 1/2 binary64)) (.f64 (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (sin.f64 th)) (.f64 (.f64 (.f64 kx kx) #s(literal -1/2 binary64)) (.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64))) (/.f64 #s(literal 1/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 ky) #s(literal 8 binary64))) (/.f64 #s(literal 2/3 binary64) (pow.f64 (sin.f64 ky) #s(literal 6 binary64)))) (/.f64 #s(literal 2/45 binary64) (pow.f64 (sin.f64 ky) #s(literal 4 binary64))))) (sin.f64 th)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 kx kx) (/.f64 (.f64 (sin.f64 th) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) (sin.f64 th))
#s(literal 1 binary64)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))
(fma.f64 (fma.f64 (/.f64 (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))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 kx (/.f64 kx (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)))) (.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (.f64 kx kx) #s(literal 1 binary64))
(sin.f64 ky)
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky))
(fma.f64 (fma.f64 (/.f64 (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))
(fma.f64 (fma.f64 (fma.f64 (.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/3 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/2 binary64) #s(literal 2/45 binary64)) (.f64 kx (/.f64 kx (sin.f64 ky)))) #s(literal 1/2 binary64) (/.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal -1/2 binary64) #s(literal -1/6 binary64)) (sin.f64 ky))) (.f64 kx kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 ky))) (.f64 kx kx) (sin.f64 ky))
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(.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 #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 ky) th) th) (sin.f64 ky)) (.f64 (.f64 (.f64 th th) (.f64 th th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (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 #s(literal -1/5040 binary64) (.f64 (*.f64 (sin.f64 ky) th) th)))))) 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 (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 -1/6 binary64) (.f64 (.f64 (sin.f64 ky) th) th) (sin.f64 ky))) th)
(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 (.f64 (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) (.f64 (.f64 (sin.f64 ky) th) th) (.f64 #s(literal -1/6 binary64) (sin.f64 ky)))) (pow.f64 th #s(literal 3 binary64))))
(.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 #s(literal -1/6 binary64) (.f64 (.f64 (sin.f64 ky) th) th) (sin.f64 ky)) (.f64 (.f64 (.f64 th th) (.f64 th th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (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 #s(literal -1/5040 binary64) (.f64 (*.f64 (sin.f64 ky) th) th)))))) th)
(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))
(/.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 1/6 binary64) (.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sin.f64 ky)))) th)
(/.f64 (fma.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 7/360 binary64) (.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 1/6 binary64) (sin.f64 ky)))) (*.f64 th th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)
(/.f64 (fma.f64 (fma.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (fma.f64 #s(literal 31/15120 binary64) (.f64 th (/.f64 th (sin.f64 ky))) (/.f64 #s(literal 7/360 binary64) (sin.f64 ky)))) (.f64 th th) (.f64 (/.f64 #s(literal 1/6 binary64) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (*.f64 th th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)
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)
(fma.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64) th)
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(*.f64 th th)
(*.f64 th th)
(*.f64 th th)
(*.f64 th th)
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64)))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(sin.f64 th)
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(.f64 (.f64 th th) #s(literal -1/6 binary64))
(*.f64 th th)
(*.f64 th th)
(*.f64 th th)
(*.f64 th th)
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 th))
(*.f64 (pow.f64 th #s(literal 3 binary64)) #s(literal -1/6 binary64))
(.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))
(.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))
(.f64 (neg.f64 (-.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (.f64 th th)))) (pow.f64 th #s(literal 3 binary64)))

rewrite206.0ms (1.9%)

Memory

19.8MiB live, 371.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	455
0	108	440
1	367	425
2	2359	425
0	9316	422

Stop Event

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

Counts

25 → 617

Calls

Call 1

Inputs
(*.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)))
(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 (.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)
(fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (*.f64 #s(literal 1/15 binary64) kx))
(fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (*.f64 #s(literal 1/3 binary64) kx))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky)))
(sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))))
(fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx)))
(fma.f64 (.f64 #s(literal -1/6 binary64) (.f64 th th)) th th)
#s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky)))
(/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))
(fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (.f64 ky ky))) #s(literal 1 binary64))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (neg.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sqrt.f64 (sin.f64 ky)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 ky) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64)) (sin.f64 ky))
(*.f64 (neg.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(*.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (sin.f64 ky) #s(literal 1 binary64)))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 ky))
(*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal 1 binary64))
(*.f64 (neg.f64 (sin.f64 ky)) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (sin.f64 ky) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (sin.f64 ky)))
(*.f64 (sin.f64 ky) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (neg.f64 (sin.f64 ky))))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(pow.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky)))) (neg.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))) (neg.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))) (*.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)) (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) #s(literal 1 binary64)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) #s(literal 1 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(/.f64 (neg.f64 (sin.f64 ky)) (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 (sin.f64 ky) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(-.f64 (/.f64 #s(literal 0 binary64) (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(exp.f64 (-.f64 (log.f64 (sin.f64 ky)) (*.f64 (log.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 th) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (/.f64 #s(literal -2 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (.f64 (sin.f64 (/.f64 (-.f64 (-.f64 th ky) (+.f64 th ky)) #s(literal 2 binary64))) (sin.f64 (/.f64 (+.f64 (-.f64 th ky) (+.f64 th ky)) #s(literal 2 binary64)))) #s(literal 2 binary64)))
(*.f64 (/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky))) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/2 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (sin.f64 th) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(.f64 (/.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (/.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (/.f64 (sin.f64 ky) #s(literal -1 binary64)) (/.f64 (neg.f64 (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))
(*.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (neg.f64 (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) #s(literal 1 binary64)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(literal 1 binary64)))
(.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (.f64 (/.f64 (sin.f64 th) #s(literal 1 binary64)) (sin.f64 ky)))
(.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (.f64 (sin.f64 th) (sin.f64 ky)) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)))
(.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 (sin.f64 ky) (.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (sin.f64 th)))
(.f64 #s(literal -1 binary64) (/.f64 (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(.f64 #s(literal -1 binary64) (.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))))
(pow.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))) #s(literal -1 binary64))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))))) (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (sin.f64 th)) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky)))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky)))) (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (-.f64 (cos.f64 (-.f64 th ky)) (cos.f64 (+.f64 th ky))) (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64)))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky)))))
(neg.f64 (*.f64 (sin.f64 th) (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(neg.f64 (*.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th)))
(-.f64 (/.f64 (cos.f64 (-.f64 th ky)) (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))) (/.f64 (cos.f64 (+.f64 th ky)) (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal 2 binary64))))
(-.f64 (/.f64 (/.f64 (cos.f64 (-.f64 th ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 (/.f64 (cos.f64 (+.f64 th ky)) #s(literal 2 binary64)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 #s(literal -1 binary64) (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(pow.f64 (/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(literal -1 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (pow.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (sqrt.f64 (pow.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 (sqrt.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 4 binary64)) (pow.f64 (sin.f64 kx) #s(literal 4 binary64)))) (pow.f64 (pow.f64 (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
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(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx) #s(literal -1 binary64)) (fma.f64 (pow.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) kx) #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (pow.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) kx) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx)))) (fma.f64 (pow.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (*.f64 ky ky) kx))) kx) #s(literal 3 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)))))
(fma.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) #s(literal -1/2 binary64)) kx #s(literal 1 binary64))
(fma.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) kx) #s(literal -1/2 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx)) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx)) #s(literal 1 binary64))
(fma.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 (*.f64 #s(literal -1/2 binary64) kx) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) kx) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (*.f64 ky ky) kx))) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (*.f64 ky ky) kx))) kx) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) kx) #s(literal 1 binary64))
(fma.f64 kx (.f64 #s(literal -1/2 binary64) #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx)))) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx)))) (/.f64 (pow.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx)))))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx)) #s(literal 2 binary64)) (fma.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (.f64 #s(literal -1/2 binary64) kx) #s(literal -1 binary64))) (pow.f64 (fma.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx) #s(literal -1 binary64)) #s(literal -1 binary64)))
(+.f64 (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx)) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 #s(approx (/ kx (pow (sin ky) 2)) (.f64 (pow.f64 ky #s(literal -2 binary64)) (fma.f64 (fma.f64 (.f64 ky ky) (fma.f64 (.f64 (.f64 (neg.f64 ky) ky) #s(literal -2/189 binary64)) kx (.f64 #s(literal 1/15 binary64) kx)) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx))) (*.f64 #s(literal -1/2 binary64) kx)))
#s(approx (pow (sin kx) 2) (*.f64 kx kx))

eval199.0ms (1.9%)

Memory: 20.6MiB live, 436.7MiB allocated
Compiler: Compiled 52 133 to 3 603 computations (93.1% saved)

prune125.0ms (1.2%)

Memory

17.3MiB live, 327.2MiB allocated

Pruning

71 alts after pruning (67 fresh and 4 done)

	Pruned	Kept	Total
New	1 206	21	1 227
Fresh	2	46	48
Picked	4	1	5
Done	0	3	3
Total	1 212	71	1 283

Accuracy

100.0%

Counts

1 283 → 71

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))
✓	97.2%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	78.5%	(/.f64 (.f64 (sin.f64 th) (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 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
	31.3%	(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
	45.7%	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
	33.0%	(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
	46.5%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	49.8%	(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	96.6%	(/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	78.1%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky)) (sin.f64 th)))
	32.4%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
	45.8%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	43.2%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	53.1%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	43.6%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	40.4%	(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
	33.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
	29.1%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
	27.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (sin.f64 th)))
	35.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	30.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
	98.7%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))))
	49.4%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
	52.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
	31.3%	(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
	31.3%	(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
	78.5%	(.f64 (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))
	33.0%	(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
	30.9%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
	27.8%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
	33.0%	(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
	78.6%	(.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))
	87.0%	(.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 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	37.7%	(.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))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
	19.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
✓	54.5%	(.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))
	46.4%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
	29.0%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
	33.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	99.4%	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) (sin.f64 ky))
	78.5%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))) (sin.f64 th))
✓	33.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	33.0%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
	30.1%	(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky))))) (sin.f64 th))
	33.0%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
	29.7%	(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
	27.7%	(.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))
	33.0%	(.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))
	33.0%	(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
	45.7%	(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
	14.0%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
	23.5%	(.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 #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
	22.9%	(.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 #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
	12.8%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
	11.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
	18.6%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
	15.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
	29.8%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	14.3%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
	15.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
	15.7%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
	3.2%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
	3.1%	(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
✓	27.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
	15.4%	#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)))
	15.4%	#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)))
	15.4%	#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)))
	15.4%	#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)))
	15.4%	#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)))
	12.6%	#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)))))
	6.5%	#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 4 602 to 1 929 computations (58.1% saved)

regimes317.0ms (3%)

Memory

-40.3MiB live, 612.9MiB allocated

Counts

98 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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 (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) ky) ky (sin.f64 kx)) ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky))))) (sin.f64 th))
(.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 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))
(/.f64 (.f64 (sin.f64 th) (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 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky)) (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 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal -1/2 binary64)) (sin.f64 th)))
(.f64 (sin.f64 ky) (.f64 (pow.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (*.f64 kx kx))) #s(literal -1/2 binary64)) (sin.f64 th)))
(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
(.f64 (neg.f64 (sin.f64 ky)) (.f64 (/.f64 #s(literal -1 binary64) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 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) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))) (sin.f64 ky))
(*.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 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal -1 binary64) (sin.f64 ky)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (neg.f64 (sin.f64 th)))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(/.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (pow.f64 (sin.f64 th) #s(literal -1 binary64)))
(/.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) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 (*.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64)) #s(literal 2 binary64))) (pow.f64 (cos.f64 kx) #s(literal 2 binary64))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

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

Calls

9 calls:

50.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
46.0ms	(sin.f64 ky)
42.0ms	(sin.f64 th)
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))
30.0ms	ky

Results

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

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes213.0ms (2%)

Memory

24.3MiB live, 506.5MiB allocated

Counts

77 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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 (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) ky) ky (sin.f64 kx)) ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky))))) (sin.f64 th))
(.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 th) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))
(/.f64 (.f64 (sin.f64 th) (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 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))))) #s(literal 2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #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 ky)) (sin.f64 th)))

Outputs

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

(*.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:

27.0ms	(sin.f64 kx)
25.0ms	ky
24.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
23.0ms	(sin.f64 th)
22.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Results

Accuracy	Segments	Branch
94.8%	2	`kx`
96.8%	2	`ky`
85.7%	2	`th`
80.8%	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))`
97.3%	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)))))`
96.9%	3	`(sin.f64 ky)`
94.8%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
94.8%	3	`(sin.f64 kx)`
85.7%	3	`(sin.f64 th)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes245.0ms (2.3%)

Memory

-25.1MiB live, 390.5MiB allocated

Counts

72 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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 (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (fma.f64 (*.f64 (fma.f64 #s(literal 1/6 binary64) (sin.f64 kx) (/.f64 #s(literal 1/2 binary64) (sin.f64 kx))) ky) ky (sin.f64 kx)) ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sqrt.f64 (sin.f64 ky))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (sin.f64 ky))))) (sin.f64 th))

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

Calls

8 calls:

65.0ms	kx
48.0ms	(sin.f64 kx)
23.0ms	ky
22.0ms	(sin.f64 th)
22.0ms	th

Results

Accuracy	Segments	Branch
77.5%	3	`(sin.f64 th)`
77.5%	2	`th`
74.5%	3	`(sin.f64 kx)`
86.2%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
74.2%	2	`kx`
74.2%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
76.6%	3	`(sin.f64 ky)`
76.5%	2	`ky`

Compiler

Compiled 26 to 38 computations (-46.2% saved)

regimes24.0ms (0.2%)

Memory

-6.5MiB live, 70.0MiB allocated

Counts

69 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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 (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) 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 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th)))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) 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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))

Calls

1 calls:

20.0ms

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

Results

Accuracy	Segments	Branch
86.2%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes24.0ms (0.2%)

Memory

-19.2MiB live, 65.0MiB allocated

Counts

68 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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 (sin ky) 2))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sin.f64 kx)) ky) ky (sin.f64 kx)))) (sin.f64 ky))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (*.f64 ky ky)))) (sin.f64 ky)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 kx kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (.f64 (sin.f64 th) (sin.f64 ky))))

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

Calls

1 calls:

19.0ms

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

Results

Accuracy	Segments	Branch
86.1%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes21.0ms (0.2%)

Memory

14.6MiB live, 52.7MiB allocated

Counts

61 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))))
(.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))

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

Calls

1 calls:

17.0ms

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

Results

Accuracy	Segments	Branch
86.0%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes20.0ms (0.2%)

Memory

16.6MiB live, 55.2MiB allocated

Counts

59 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 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))

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

Calls

1 calls:

17.0ms

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

Results

Accuracy	Segments	Branch
85.9%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes77.0ms (0.7%)

Memory

-3.4MiB live, 77.0MiB allocated

Counts

58 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

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

Calls

2 calls:

40.0ms

(/.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

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

Results

Accuracy	Segments	Branch
67.0%	4	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
85.4%	5	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 29 to 24 computations (17.2% saved)

regimes22.0ms (0.2%)

Memory

7.1MiB live, 42.7MiB allocated

Counts

57 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (*.f64 (sin.f64 ky) th))))
(.f64 (pow.f64 (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) #s(literal -1 binary64)) (/.f64 (sin.f64 th) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))

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

Calls

1 calls:

19.0ms

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

Results

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes21.0ms (0.2%)

Memory

4.1MiB live, 40.7MiB allocated

Counts

55 → 5

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

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

Calls

1 calls:

17.0ms

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

Results

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

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes127.0ms (1.2%)

Memory

-0.3MiB live, 281.0MiB allocated

Counts

54 → 6

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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))
(/.f64 #s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

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

Calls

7 calls:

21.0ms	th
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)))))
18.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
17.0ms	ky
17.0ms	kx

Results

Accuracy	Segments	Branch
69.4%	5	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
70.6%	5	`kx`
71.4%	4	`(sin.f64 ky)`
68.3%	3	`(sin.f64 th)`
71.4%	3	`ky`
68.3%	2	`th`
80.1%	6	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 24 to 34 computations (-41.7% saved)

regimes111.0ms (1%)

Memory

-9.3MiB live, 220.0MiB allocated

Counts

53 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) kx)) #s(literal 1/2 binary64))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky))) #s(literal 1/2 binary64) #s(approx (pow (sin kx) 2) (.f64 kx kx)))) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (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))) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 (.f64 (sin.f64 th) (pow.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64))) (sin.f64 ky))
(.f64 (pow.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) #s(literal -1 binary64)) (*.f64 (sin.f64 th) (sin.f64 ky)))

Outputs

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

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

Calls

6 calls:

23.0ms	ky
18.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
17.0ms	(sin.f64 th)
17.0ms	(sin.f64 ky)
17.0ms	th

Results

Accuracy	Segments	Branch
50.1%	2	`(sin.f64 th)`
69.5%	4	`(sin.f64 ky)`
50.4%	2	`th`
68.0%	3	`ky`
67.4%	4	`(sin.f64 kx)`
68.9%	4	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 21 to 29 computations (-38.1% saved)

regimes67.0ms (0.6%)

Memory

21.4MiB live, 136.4MiB allocated

Counts

48 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64)))))) (sin.f64 th))

Outputs

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

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

4 calls:

20.0ms	ky
15.0ms	(sin.f64 ky)
15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
14.0ms	kx

Results

Accuracy	Segments	Branch
66.7%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`
58.1%	3	`kx`
62.3%	4	`(sin.f64 ky)`
60.8%	3	`ky`

Compiler

Compiled 17 to 21 computations (-23.5% saved)

regimes125.0ms (1.2%)

Memory

2.5MiB live, 282.0MiB allocated

Counts

47 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky))
(.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky))) (sin.f64 ky))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))
(/.f64 (.f64 (sin.f64 th) (sin.f64 ky)) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 ky)))
(/.f64 (sin.f64 th) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)))
(.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 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 kx)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (pow (sin kx) 2))) (sin.f64 ky)) (*.f64 (sin.f64 th) (sin.f64 ky))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 #s(literal -1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)) (sin.f64 ky)) (sin.f64 th)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 ky) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64)))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 th) (neg.f64 #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 ky))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (fma.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))) (*.f64 kx kx) #s(literal 1 binary64))) (sin.f64 th)))

Outputs

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

7 calls:

30.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
18.0ms	(sin.f64 ky)
16.0ms	(sin.f64 kx)
15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
14.0ms	kx

Results

Accuracy	Segments	Branch
45.3%	2	`kx`
49.7%	3	`(sin.f64 ky)`
47.8%	3	`ky`
45.1%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
46.1%	2	`(sin.f64 kx)`
45.3%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
53.1%	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 39 to 44 computations (-12.8% saved)

regimes11.0ms (0.1%)

Memory

-11.7MiB live, 27.5MiB allocated

Counts

30 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))

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:

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
53.1%	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)

regimes11.0ms (0.1%)

Memory

-10.7MiB live, 28.7MiB allocated

Counts

29 → 2

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.f64 th) #s(literal 3 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 (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) #s(approx (/ (+ (* (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (* ky ky)) kx) (* ky ky)) (.f64 (.f64 (pow.f64 ky #s(literal 4 binary64)) kx) #s(literal 2/189 binary64)))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 (/.f64 #s(literal 1 binary64) #s(approx (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky))) (sin.f64 th))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (/.f64 (sin.f64 kx) ky)) (sin.f64 th)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) #s(approx (pow (sin ky) 2) (*.f64 ky ky))))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (/.f64 (.f64 (.f64 #s(literal -1/2 binary64) kx) kx) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 #s(literal 2 binary64) ky)))) #s(literal 2 binary64) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (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)))) #s(literal 1 binary64))) (sin.f64 th))

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:

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
50.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes96.0ms (0.9%)

Memory

-1.1MiB live, 118.8MiB allocated

Counts

22 → 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 (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)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) #s(literal 1 binary64)) (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 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 th th)) #s(literal 1/6 binary64)) (pow.f64 th #s(literal 3 binary64))))))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (.f64 kx (/.f64 kx (*.f64 ky ky))) #s(literal -1/2 binary64)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) (/.f64 kx #s(approx (pow (sin ky) 2) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) kx) ky) (/.f64 kx ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 ky ky (.f64 (.f64 kx kx) (fma.f64 (.f64 #s(literal -1/6 binary64) ky) ky #s(literal -1/2 binary64)))) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) kx) kx (.f64 (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 kx kx) #s(literal 1 binary64)) ky) ky)) (*.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (/.f64 (fma.f64 (.f64 (.f64 ky ky) kx) #s(literal 1/3 binary64) kx) ky) ky)) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (neg.f64 (.f64 (.f64 kx (fma.f64 #s(literal -1/15 binary64) (.f64 ky ky) #s(literal -1/3 binary64))) ky)) ky kx) (.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 #s(approx (+ (* (+ (* (neg ky) (* ky (* kx -2/189))) (* 1/15 kx)) (* ky ky)) (* 1/3 kx)) (.f64 (fma.f64 (fma.f64 (.f64 ky ky) #s(literal 2/189 binary64) #s(literal 1/15 binary64)) (.f64 ky ky) #s(literal 1/3 binary64)) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(approx (+ ( (* -1/2 kx) (/ kx (pow (sin ky) 2))) 1) (/.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) kx) kx (fma.f64 (.f64 (.f64 kx kx) #s(literal -1/30 binary64)) (.f64 ky ky) #s(literal 1 binary64))) (.f64 ky ky) (.f64 (.f64 #s(literal -1/2 binary64) kx) kx)) (.f64 ky ky)))) (sin.f64 th))
(.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (fma.f64 (.f64 #s(literal -1/2 binary64) kx) #s(approx (/ kx (pow (sin ky) 2)) (/.f64 (fma.f64 (fma.f64 (fma.f64 (neg.f64 ky) (.f64 ky (.f64 kx #s(literal -2/189 binary64))) (.f64 #s(literal 1/15 binary64) kx)) (.f64 ky ky) (.f64 #s(literal 1/3 binary64) kx)) (.f64 ky ky) kx) (*.f64 ky ky))) #s(literal 1 binary64))) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) (fma.f64 (pow.f64 (pow.f64 th #s(literal 3/2 binary64)) #s(literal 2 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 (exp.f64 (*.f64 (log.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

9 calls:

23.0ms	(sin.f64 kx)
22.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
8.0ms	th
7.0ms	(sin.f64 th)
7.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
36.5%	3	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
33.0%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
33.0%	2	`kx`
33.3%	3	`(sin.f64 kx)`
31.6%	2	`ky`
32.2%	2	`(sin.f64 ky)`
32.8%	3	`(sin.f64 th)`
32.8%	2	`th`
36.3%	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)

regimes26.0ms (0.2%)

Memory

21.5MiB live, 59.1MiB 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

9 calls:

5.0ms	(sin.f64 ky)
3.0ms	(*.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	(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	kx

Results

Accuracy	Segments	Branch
27.8%	1	`(sin.f64 th)`
27.8%	1	`ky`
27.8%	1	`(sin.f64 kx)`
27.8%	1	`(sin.f64 ky)`
27.8%	1	`th`
27.8%	1	`kx`
27.8%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
27.8%	1	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
27.8%	1	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes24.0ms (0.2%)

Memory

10.2MiB live, 50.3MiB 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:

6.0ms	(sin.f64 ky)
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	kx
2.0ms	(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)))))

Results

Accuracy	Segments	Branch
15.4%	1	`kx`
15.4%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
15.4%	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)))))`
15.4%	1	`ky`
15.4%	1	`th`
15.4%	1	`(sin.f64 ky)`
15.4%	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))`
15.4%	1	`(sin.f64 th)`
15.4%	1	`(sin.f64 kx)`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

bsearch20.0ms (0.2%)

Memory

3.7MiB live, 41.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
18.0ms	6.995202715896866e-10	3.714935695575888e-9

Samples

12.0ms

96×

valid

Compiler

Compiled 265 to 222 computations (16.2% saved)

Precisions

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

ival-sin: 5.0ms (52.1% of total)

ival-pow2: 2.0ms (20.8% of total)

ival-div: 1.0ms (10.4% of total)

ival-mult: 1.0ms (10.4% of total)

ival-sqrt: 1.0ms (10.4% of total)

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

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

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

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.994405689307552	0.9999991003006525
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.23237783708566676	-0.17011595632917087
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.994405689307552	0.9999991003006525
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.23237783708566676	-0.17011595632917087
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch3.0ms (0%)

Memory

-36.2MiB live, 2.4MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.994405689307552	0.9999991003006525
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.338852757653229	-0.23237783708566676
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.338852757653229	-0.23237783708566676
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.338852757653229	-0.23237783708566676
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.17011595632917087	1.2857764289785268e-304
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.17011595632917087	1.2857764289785268e-304
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

4×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	-0.17011595632917087	1.2857764289785268e-304
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

3.0MiB live, 3.0MiB allocated

Algorithm

5×	left-value

Steps

Time	Left	Right
0.0ms	0.9037559472110506	0.9054949561885188
0.0ms	3.368539857948204e-8	0.2450263012802989
0.0ms	2.05604678797736e-56	3.363169470194084e-56
0.0ms	-0.338852757653229	-0.23237783708566676
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch51.0ms (0.5%)

Memory

-12.9MiB live, 82.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
28.0ms	3.714935695575888e-9	0.0030824925020382743
20.0ms	2.456163153706155e-145	2.863453614397872e-143

Samples

36.0ms

256×

valid

Compiler

Compiled 766 to 655 computations (14.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sin: 14.0ms (48.4% of total)

ival-pow2: 8.0ms (27.7% of total)

ival-div: 2.0ms (6.9% of total)

ival-mult: 2.0ms (6.9% of total)

ival-sqrt: 2.0ms (6.9% of total)

ival-add: 1.0ms (3.5% of total)

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

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

bsearch1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.4249661023211534	0.43696945438187973
0.0ms	-0.9997487469761014	-0.9988290925473484

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.4249661023211534	0.43696945438187973

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.4249661023211534	0.43696945438187973

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.368539857948204e-8	0.2450263012802989

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4034919855283681e-39	4.8387758389196477e-32

Compiler

Compiled 19 to 19 computations (0% saved)

simplify37.0ms (0.3%)

Memory

-2.8MiB live, 75.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	193	2133
1	239	2133
2	261	2133
3	271	2133
4	277	2133
5	278	2133

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(if (<=.f64 ky #s(literal 279564095785883/75557863725914323419136 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.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 (/.f64 (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 -8998192055486251/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 th) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/18889465931478580854784 binary64)) (.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 (sin.f64 ky) 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 ky)) kx) kx (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 -8998192055486251/9007199254740992 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 -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 944473296573929/18889465931478580854784 binary64)) (.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky)))))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 (sin.f64 ky) 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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
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#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 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
(if (<=.f64 ky #s(literal 279564095785883/75557863725914323419136 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (.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 (/.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 -8998192055486251/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(approx (+ (* (sin ky) (sin ky)) (pow (sin kx) 2)) (fma.f64 (.f64 (fma.f64 #s(literal -1/3 binary64) (.f64 kx kx) #s(literal 1 binary64)) kx) kx (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (.f64 (sin.f64 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 -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64))) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (sin.f64 ky))))) (.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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -8998192055486251/9007199254740992 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 -3602879701896397/18014398509481984 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)) (fma.f64 (.f64 th th) #s(literal 1/6 binary64) #s(literal 1 binary64))) th))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (sin.f64 ky))))) (.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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -8998192055486251/9007199254740992 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 -5404319552844595/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 8962163258467287/9007199254740992 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (sin.f64 ky))))) (.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 ky)) kx) kx (sin.f64 ky)))) (sin.f64 th))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -8998192055486251/9007199254740992 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 -5404319552844595/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4075757662770299/4503599627370496 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (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 -8998192055486251/9007199254740992 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 -5404319552844595/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin ky) 2) (.f64 ky ky)) (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 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4075757662770299/4503599627370496 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (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 -8998192055486251/9007199254740992 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 -3602879701896397/36028797018963968 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 4075757662770299/4503599627370496 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (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 -8998192055486251/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) #s(approx (pow (sin kx) 2) (.f64 kx kx))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 4075757662770299/4503599627370496 binary64)) (/.f64 #s(literal 1 binary64) #s(approx (/ (/ (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin ky)) (sin th)) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (.f64 th (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 -8998192055486251/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) #s(approx (pow (sin kx) 2) (.f64 kx kx))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal -3602879701896397/36028797018963968 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 944473296573929/18889465931478580854784 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 (sin.f64 th) ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 4075757662770299/4503599627370496 binary64)) (/.f64 #s(approx ( (sin th) (sin ky)) (.f64 th (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))))))
(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 -8998192055486251/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) #s(approx (pow (sin kx) 2) (.f64 kx kx))))) (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 -5404319552844595/18014398509481984 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (sin.f64 ky))) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (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 6625676492918941/220855883097298041197912187592864814478435487109452369765200775161577472 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 944473296573929/18889465931478580854784 binary64)) (.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))))) #s(literal 4075757662770299/4503599627370496 binary64)) (/.f64 #s(approx (* (sin th) (sin ky)) (.f64 th (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)))))))
(if (<=.f64 ky #s(literal 439347050248359/1757388200993436087035366604564836663620975436836686184804982645551499054949799949343375268009332366074187855716219099657503228927927460816018951242525454630912 binary64)) (.f64 (/.f64 (sin.f64 th) #s(approx (sqrt (+ ( (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sin.f64 kx))) (sin.f64 ky)) (if (<=.f64 ky #s(literal 3458764513820541/1152921504606846976 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) kx)))) #s(approx (pow (sin ky) 2) (.f64 ky ky))))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) #s(approx (pow (sin kx) 2) (.f64 kx kx))))) (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 -8998192055486251/9007199254740992 binary64)) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 #s(literal 1/2 binary64) (.f64 (cos.f64 (.f64 #s(literal 2 binary64) ky)) #s(literal 1/2 binary64))) #s(approx (pow (sin kx) 2) (.f64 kx kx))))) (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 7746191359077253/18014398509481984 binary64)) (.f64 (/.f64 (sin.f64 th) #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 7746191359077253/18014398509481984 binary64)) (.f64 (/.f64 (sin.f64 th) #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 7746191359077253/18014398509481984 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 944473296573929/18889465931478580854784 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 6129982163463555/3064991081731777716716694054300618367237478244367204352 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)))

soundness1.6s (14.9%)

Memory

47.3MiB live, 1 655.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	160
0	54	153
1	183	153
2	1099	153
0	8204	153
0	624	12516
1	1984	12113
2	7537	12113
0	8295	11156
0	42	241
0	70	222
1	239	222
2	1425	222
0	8253	222
0	529	10392
1	1693	10038
2	6497	9737
0	8053	9172
0	518	9344
1	1671	8918
2	6197	8588
0	8691	7946
0	317	2263
1	1011	2214
2	3847	2122
3	7794	2122
0	8097	1974
0	13	49
0	22	49
1	62	49
2	338	49
3	2902	49
0	8284	34

Stop Event

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

Compiler

Compiled 4 191 to 1 462 computations (65.1% saved)

preprocess169.0ms (1.6%)

Memory

-28.3MiB live, 293.8MiB allocated

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 4 430 to 522 computations (88.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	42	300
0	70	287
1	102	283
2	139	281
3	222	281
4	311	281
5	354	281
6	354	281
7	375	281
8	375	281
0	375	281

Iter	Nodes	Cost
0	42	300
0	70	287
1	102	283
2	139	281
3	222	281
4	311	281
5	354	281
6	354	281
7	375	281
8	375	281
0	375	281

start0.0ms (0%)

analyze197.0ms (1.8%)

sample2.0s (19%)

explain290.0ms (2.7%)

preprocess130.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0%)

localize111.0ms (1%)

series63.0ms (0.6%)

simplify244.0ms (2.3%)

rewrite220.0ms (2.1%)

eval97.0ms (0.9%)

prune118.0ms (1.1%)

simplify8.0ms (0.1%)

localize154.0ms (1.4%)

series49.0ms (0.5%)

simplify212.0ms (2%)

rewrite347.0ms (3.2%)

eval375.0ms (3.5%)

prune97.0ms (0.9%)

simplify16.0ms (0.2%)

localize114.0ms (1.1%)

series99.0ms (0.9%)

simplify247.0ms (2.3%)

rewrite172.0ms (1.6%)

eval267.0ms (2.5%)

prune136.0ms (1.3%)

simplify128.0ms (1.2%)

localize439.0ms (4.1%)

series59.0ms (0.5%)

simplify276.0ms (2.6%)

rewrite206.0ms (1.9%)

eval199.0ms (1.9%)

prune125.0ms (1.2%)

regimes317.0ms (3%)

regimes213.0ms (2%)

regimes245.0ms (2.3%)

regimes24.0ms (0.2%)

regimes24.0ms (0.2%)

regimes21.0ms (0.2%)

regimes20.0ms (0.2%)

regimes77.0ms (0.7%)

regimes22.0ms (0.2%)

regimes21.0ms (0.2%)

regimes127.0ms (1.2%)

regimes111.0ms (1%)

regimes67.0ms (0.6%)

regimes125.0ms (1.2%)

regimes11.0ms (0.1%)

regimes11.0ms (0.1%)

regimes96.0ms (0.9%)

regimes26.0ms (0.2%)

regimes24.0ms (0.2%)

bsearch20.0ms (0.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch3.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch51.0ms (0.5%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify37.0ms (0.3%)

soundness1.6s (14.9%)

preprocess169.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	42	300
0	70	287
1	102	283
2	139	281
3	222	281
4	311	281
5	354	281
6	354	281
7	375	281
8	375	281
0	375	281