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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze194.0ms (1.4%)

Memory

-5.7MiB live, 322.3MiB allocated; 29ms collecting garbage

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)

sample4.0s (29.8%)

Memory

26.3MiB live, 2 251.8MiB allocated; 1.1s collecting garbage

Samples

2.8s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 2.5s

ival-sin: 2.0s (77.8% of total)

ival-pow2: 285.0ms (11.3% of total)

ival-mult: 103.0ms (4.1% of total)

ival-sqrt: 61.0ms (2.4% of total)

ival-div: 52.0ms (2.1% of total)

ival-add: 47.0ms (1.9% of total)

ival-true: 6.0ms (0.2% of total)

adjust: 3.0ms (0.1% of total)

ival-assert: 3.0ms (0.1% of total)

Bogosity

explain207.0ms (1.5%)

Memory

8.2MiB live, 200.1MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
23	-	4	(-2.1127173540015023e-273 -2.752346614208405e-162 6.742563595767909e+279)	`(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	19	0
↳	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`	underflow	55
↳	`(pow.f64 (sin.f64 ky) #s(literal 2 binary64))`	underflow	69
↳	`(+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))`	underflow	19

Confusion

	Predicted +	Predicted -
+	19	4
-	0	233

Precision

1.0

Recall

0.8260869565217391

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	19	0	4
-	0	0	233

Precision?

1.0

Recall?

0.8260869565217391

Freqs

test

number	freq
0	237
1	19

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

87.0ms

512×

valid

Compiler

Compiled 152 to 43 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-sin: 31.0ms (45.6% of total)

ival-pow2: 24.0ms (35.3% of total)

ival-div: 3.0ms (4.4% of total)

ival-mult: 3.0ms (4.4% of total)

ival-sqrt: 3.0ms (4.4% of total)

ival-add: 2.0ms (2.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess375.0ms (2.8%)

Memory

35.1MiB live, 79.8MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	153
1	102	147
2	237	147
3	448	147
4	972	147
5	3032	147
0	18	20
0	25	20
1	27	20
2	30	20
3	35	20
4	55	20
5	132	20
6	585	20
7	4699	20
0	8431	20

Stop Event

1×	saturated
1×	node limit
1×	iter limit
1×	node 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))

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

Symmetry

(abs kx)

(negabs th)

(negabs ky)

Compiler

Compiled 16 to 13 computations (18.8% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.4%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))

Compiler

Compiled 16 to 13 computations (18.8% saved)

simplify125.0ms (0.9%)

Memory

-1.9MiB live, 45.8MiB allocated; 14ms collecting garbage

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	88
0	25	88
1	27	88
2	30	88
3	35	88
4	55	88
5	132	88
6	585	88
7	4699	88
0	8431	88

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize391.0ms (2.9%)

Memory

-27.7MiB live, 64.5MiB allocated; 7ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.19921875	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.26009750976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	0.3170700195368841	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
accuracy	5.131981369608339	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))

Samples

382.0ms

256×

valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 373.0ms

ival-sin: 345.0ms (92.6% of total)

ival-pow2: 21.0ms (5.6% of total)

ival-mult: 2.0ms (0.5% of total)

ival-sqrt: 2.0ms (0.5% of total)

ival-div: 1.0ms (0.3% of total)

ival-add: 1.0ms (0.3% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.2%)

Memory

10.5MiB live, 54.3MiB allocated; 8ms collecting garbage

Counts

6 → 46

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

Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (pow kx 2)))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (pow (sin kx) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow ky 2)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow (sin ky) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (pow (sin ky) 2))
5.0ms	th	@	0	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (pow (sin ky) 2))
4.0ms	th	@	-inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (pow (sin ky) 2))
3.0ms	kx	@	inf	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (pow (sin ky) 2))
3.0ms	kx	@	0	((* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (pow (sin kx) 2) (pow (sin ky) 2))

simplify520.0ms (3.8%)

Memory

2.4MiB live, 195.0MiB allocated; 32ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	414	2005
1	1244	1939
2	5716	1912
0	8948	1869
1	10596	1869
2	14848	1869
3	19184	1869
4	22082	1869
5	23778	1869
6	25006	1869
7	25597	1869
8	25642	1869

Stop Event

1×	saturated
1×	node limit

Counts

46 → 12

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (pow kx 2)))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* -1/3 (pow kx 2))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* 2/45 (pow kx 2)) 1/3))))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (* (pow kx 2) (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 2/45 (* -1/315 (pow kx 2)))) 1/3))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (pow (sin kx) 2) #s(hole binary64 (pow (sin kx) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow ky 2)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow (sin ky) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))

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

rewrite70.0ms (0.5%)

Memory

1.4MiB live, 100.3MiB allocated; 11ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	65
1	25	65
2	31	65
3	35	59
4	37	59
5	39	59
6	41	59
7	43	59
0	43	59
1	80	59
0	362	36
1	509	36
2	680	36
3	833	36
4	896	36
5	908	36
6	909	36

Stop Event

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

Counts

6 → 66

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

Outputs
(*.f64 (sin.f64 th) (/.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))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (neg.f64 (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (sin.f64 th) (sin.f64 ky))) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(sin.f64 ky)
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (*.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(*.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 kx)))
(*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx)))
(*.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 kx))))
(*.f64 (sin.f64 kx) (sin.f64 kx))
(pow.f64 (exp.f64 (log.f64 (sin.f64 kx))) #s(literal 2 binary64))
(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))))
(*.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 ky)))
(*.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 ky))))
(*.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 ky)))
(*.f64 (sin.f64 ky) (sin.f64 ky))
(pow.f64 (exp.f64 (log.f64 (sin.f64 ky))) #s(literal 2 binary64))
(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 ky ky)) (cos.f64 (+.f64 ky ky))) #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (sin.f64 ky)) #s(literal 2 binary64))))

eval9.0ms (0.1%)

Memory: 15.5MiB live, 15.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 328 to 323 computations (75.7% saved)

prune48.0ms (0.4%)

Memory

-26.7MiB live, 20.3MiB allocated; 2ms collecting garbage

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	66	15	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	66	16	82

Accuracy

99.9%

Counts

82 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	95.5%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
▶	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	76.9%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) (sin.f64 th))
	83.3%	(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)))))) (sin.f64 th))
	42.7%	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th))
	91.5%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	91.4%	(*.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))
	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))
▶	85.2%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	47.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	48.6%	(.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))
▶	34.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	31.7%	(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
	29.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
▶	31.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))

Compiler

Compiled 646 to 453 computations (29.9% saved)

simplify96.0ms (0.7%)

Memory

20.2MiB live, 67.0MiB allocated; 3ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx 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 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
cost-diff	0	(sin.f64 th)
cost-diff	0	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
cost-diff	0	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
cost-diff	0	(sin.f64 ky)
cost-diff	0	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
cost-diff	0	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (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	42	289
0	52	289
1	60	289
2	83	289
3	143	289
4	268	289
5	615	289
6	2369	289
7	7584	289
0	8124	289

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize182.0ms (1.3%)

Memory

31.9MiB live, 302.1MiB allocated; 32ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.19921875	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
accuracy	0.26009750976844204	(pow.f64 (sin.f64 ky) #s(literal 2 binary64))
accuracy	5.131981369608339	(sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	13.599624729389923	(-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.21484375	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
accuracy	0.296875	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.15234375	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
accuracy	0.19921875	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
accuracy	43.489944885919265	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
accuracy	0.0	(sin.f64 th)
accuracy	44.005256250039345	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.15234375	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
accuracy	0.19921875	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Samples

57.0ms	142×	0	valid
47.0ms	72×	1	valid
34.0ms	42×	2	valid

Compiler

Compiled 299 to 31 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

ival-sin: 29.0ms (25.9% of total)

ival-cos: 22.0ms (19.6% of total)

ival-div: 15.0ms (13.4% of total)

ival-hypot: 10.0ms (8.9% of total)

adjust: 9.0ms (8% of total)

ival-mult: 8.0ms (7.1% of total)

ival-pow2: 6.0ms (5.4% of total)

ival-sqrt: 5.0ms (4.5% of total)

ival-add: 4.0ms (3.6% of total)

ival-sub: 3.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series90.0ms (0.7%)

Memory

-37.6MiB live, 155.4MiB allocated; 74ms collecting garbage

Counts

18 → 157

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
33.0ms	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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (- (cos (- kx kx)) (cos (+ kx kx))) (pow (sin ky) 2))
12.0ms	kx	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (- (cos (- kx kx)) (cos (+ kx kx))) (pow (sin ky) 2))
10.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin th) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (- (cos (- kx kx)) (cos (+ kx kx))) (pow (sin ky) 2))
6.0ms	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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (- (cos (- kx kx)) (cos (+ kx kx))) (pow (sin ky) 2))
5.0ms	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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (- (cos (- kx kx)) (cos (+ kx kx))) (pow (sin ky) 2))

simplify834.0ms (6.1%)

Memory

30.4MiB live, 259.3MiB allocated; 46ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	878	8741
1	2536	8279
0	9377	8177
1	11137	8154
2	15710	8154
3	20566	8154
4	23252	8154
5	24658	8154
6	25478	8154
7	25756	8154
8	26040	8154
9	26162	8154
10	26173	8154

Stop Event

1×	saturated
1×	node limit

Counts

157 → 30

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (* 2 (pow kx 2))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (* (pow kx 2) (+ 2 (* -2/3 (pow kx 2))))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* 4/45 (pow kx 2)) 2/3))))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (* (pow kx 2) (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 4/45 (* -2/315 (pow kx 2)))) 2/3))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (- 1 (cos (* 2 kx)))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (- 1 (cos (neg (* -2 kx))))) (pow (sin ky) 2)))))
#s(approx (- (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (- 1 (cos (neg (* -2 kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* ky (* (sin th) (sqrt 2))) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (* (sin th) (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (* ky (sqrt 2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx))))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* 1/120 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (+ (* 1/2 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (* (pow (sqrt 2) 2) (- 1 (cos (* 2 kx)))))) (+ (* 8/45 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (+ (* 2 (/ (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (- 1 (cos (* 2 kx))))) (* 8/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/12 (* (/ (- (+ (* 4/3 (/ 1 (pow (- 1 (cos (* 2 kx))) 2))) (* 8 (/ 1 (pow (- 1 (cos (* 2 kx))) 3)))) (* 4 (/ 1 (* (pow (sqrt 2) 2) (pow (- 1 (cos (* 2 kx))) 3))))) (sqrt 2)) (sqrt (- 1 (cos (* 2 kx)))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ 1 (pow (- 1 (cos (* 2 kx))) 3))))) (* -1/5040 (* (sqrt 2) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx)))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))
#s(approx (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (- 1 (cos (* 2 kx))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (+ 1/3 (* 1/4 (/ 1 (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx))))))) (* (pow (sqrt 1/2) 2) (- 1 (cos (* 2 kx)))))))) (sqrt 1/2)) (sqrt (/ 1 (- 1 (cos (* 2 kx))))))))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow ky 2)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* -1/3 (pow ky 2))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* 2/45 (pow ky 2)) 1/3))))))
#s(approx (pow (sin ky) 2) #s(hole binary64 (* (pow ky 2) (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 2/45 (* -1/315 (pow ky 2)))) 1/3))))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (pow (sin ky) 2) #s(hole binary64 (pow (sin ky) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (- (cos (- kx kx)) (cos (+ kx kx))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (- 1 (cos (* 2 kx)))) (pow (sin ky) 2))))))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))

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

rewrite41.0ms (0.3%)

Memory

13.8MiB live, 58.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	208
1	52	208
2	59	208
3	72	208
4	78	208
5	84	202
6	86	202
7	88	202
8	90	202
9	92	202
0	92	160
0	236	159
1	357	159
2	424	159
3	456	159
4	467	159
5	469	159

Stop Event

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

Counts

18 → 93

Calls

Call 1

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

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

eval21.0ms (0.2%)

Memory: -28.4MiB live, 28.1MiB allocated; 14ms collecting garbage
Compiler: Compiled 1 732 to 283 computations (83.7% saved)

prune20.0ms (0.2%)

Memory

-4.9MiB live, 40.9MiB allocated; 6ms collecting garbage

Pruning

26 alts after pruning (20 fresh and 6 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	4	6	10
Picked	0	5	5
Done	0	1	1
Total	88	26	114

Accuracy

99.9%

Counts

114 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.5%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
▶	49.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
	76.9%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) (sin.f64 th))
	56.8%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) kx))) (sin.f64 th))
	53.9%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) (sin.f64 th))
	42.7%	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th))
	91.5%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	91.4%	(*.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))
	84.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	85.2%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	41.4%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) th))
	47.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	34.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶	22.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
	22.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) (sin.f64 th))
	31.7%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	53.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
▶	56.7%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	49.5%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	31.2%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 ky))))
	34.9%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
	29.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
✓	31.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
▶	15.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))

Compiler

Compiled 895 to 645 computations (27.9% saved)

simplify102.0ms (0.8%)

Memory

33.5MiB live, 75.7MiB allocated; 11ms collecting garbage

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	195
0	44	195
1	52	195
2	75	195
3	135	195
4	260	195
5	607	195
6	2353	195
7	7560	195
0	8100	195

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize97.0ms (0.7%)

Memory

-3.4MiB live, 138.3MiB allocated; 31ms collecting garbage

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
accuracy	0.15234375	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
accuracy	0.19921875	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
accuracy	32.2496672933117	#s(approx (sin th) th)
accuracy	0.05078125	(hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))
accuracy	0.21484375	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
accuracy	0.296875	(/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))
accuracy	33.823120718490735	#s(approx (sin kx) kx)
accuracy	0.15234375	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
accuracy	0.19921875	(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
accuracy	32.2496672933117	#s(approx (sin th) th)
accuracy	43.489944885919265	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
accuracy	32.2496672933117	#s(approx (sin th) th)
accuracy	44.005256250039345	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.05078125	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.24609375	(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy	2.9126349285202178	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

Samples

79.0ms

256×

valid

Compiler

Compiled 221 to 22 computations (90% saved)

Precisions

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

ival-sin: 23.0ms (36.5% of total)

ival-hypot: 15.0ms (23.8% of total)

ival-mult: 9.0ms (14.3% of total)

ival-pow2: 8.0ms (12.7% of total)

ival-div: 5.0ms (7.9% of total)

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

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

adjust: 0.0ms (0% of total)

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

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

series26.0ms (0.2%)

Memory

1.9MiB live, 46.9MiB allocated; 8ms collecting garbage

Counts

18 → 134

Calls

Call 1

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

Outputs
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (sin th)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (sin th))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* (sin ky) (sin th))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (sin ky))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	ky	@	-inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
2.0ms	kx	@	inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
2.0ms	ky	@	inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
2.0ms	kx	@	-inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
2.0ms	th	@	inf	((/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (sin ky) (* (/ (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 ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin kx) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

simplify468.0ms (3.4%)

Memory

-28.0MiB live, 156.6MiB allocated; 94ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	624	6784
1	1755	6438
0	8027	6318
1	9280	6302
2	13211	6302
3	17200	6302
4	19187	6302
5	20185	6302
6	20647	6302
7	20718	6302
8	20724	6302

Stop Event

1×	saturated
1×	node limit

Counts

134 → 30

Calls

Call 1

Inputs
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (sin th)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (sin th))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* (sin ky) (sin th))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (sin ky))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))

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

rewrite87.0ms (0.6%)

Memory

6.0MiB live, 95.0MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	162
1	44	162
2	47	162
3	57	162
4	61	162
0	61	162
1	156	162
0	988	162
1	1160	162
2	1389	162
3	1885	162
4	2408	162
5	2631	162
6	2691	162
7	2702	162

Stop Event

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

Counts

18 → 234

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (neg.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (sin.f64 ky)) (sin.f64 th)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(*.f64 (sin.f64 ky) (sin.f64 th))
(*.f64 (sin.f64 th) (sin.f64 ky))
(sin.f64 th)
(sin.f64 ky)
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))
#s(approx (sin th) th)
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
(/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) #s(approx (sin th) th))
(/.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(neg.f64 (/.f64 (neg.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(neg.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))) (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))) (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx))))) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx)) (.f64 (sin.f64 kx) (sin.f64 kx)) (.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky)) (.f64 (sin.f64 ky) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx) (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx)))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx)) (.f64 (sin.f64 kx) (sin.f64 kx)) (.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky)) (.f64 (sin.f64 ky) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky) (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (*.f64 (sin.f64 ky) (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))) (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))))
(/.f64 (sqrt.f64 (.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))) (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx))))) (sqrt.f64 (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx)))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx)) (.f64 (sin.f64 kx) (sin.f64 kx)) (.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky)) (.f64 (sin.f64 ky) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx) (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (fma.f64 (sin.f64 ky) (sin.f64 ky) (.f64 (neg.f64 (sin.f64 kx)) (sin.f64 kx)))))))
(/.f64 (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (sin.f64 kx)) (sin.f64 kx)) (.f64 (sin.f64 kx) (sin.f64 kx)) (.f64 (.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky)) (.f64 (sin.f64 ky) (sin.f64 ky))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (sin.f64 ky) (.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (neg.f64 (sin.f64 ky)) (sin.f64 ky)))))))
(sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (*.f64 (sin.f64 ky) (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (neg.f64 (sin.f64 ky)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 kx))) (sin.f64 ky))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (neg.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (neg.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (neg.f64 (sin.f64 ky)))
(hypot.f64 (fabs.f64 (sin.f64 kx)) (sin.f64 ky))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (fabs.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (exp.f64 (log.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (fabs.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (neg.f64 (sin.f64 ky))) (sin.f64 kx))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (neg.f64 (sin.f64 ky)) (neg.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (neg.f64 (sin.f64 ky)) (sin.f64 kx))
(hypot.f64 (sin.f64 kx) (neg.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (fabs.f64 (fabs.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (exp.f64 (log.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (fabs.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (neg.f64 (neg.f64 (sin.f64 ky))))
(hypot.f64 (sin.f64 kx) (neg.f64 (sin.f64 ky)))
(hypot.f64 (sin.f64 kx) (sin.f64 ky))
(hypot.f64 (sin.f64 ky) (neg.f64 (neg.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (fabs.f64 (fabs.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))
(hypot.f64 (sin.f64 ky) (neg.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (fabs.f64 (sin.f64 kx)))
(hypot.f64 (sin.f64 ky) (sin.f64 kx))
(sin.f64 kx)
#s(approx (sin kx) kx)
(hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))

eval51.0ms (0.4%)

Memory: -9.5MiB live, 45.1MiB allocated; 12ms collecting garbage
Compiler: Compiled 2 902 to 495 computations (82.9% saved)

prune78.0ms (0.6%)

Memory

-4.3MiB live, 43.1MiB allocated; 1ms collecting garbage

Pruning

32 alts after pruning (21 fresh and 11 done)

	Pruned	Kept	Total
New	163	9	172
Fresh	3	12	15
Picked	0	5	5
Done	0	6	6
Total	166	32	198

Accuracy

99.9%

Counts

198 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	95.5%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
▶	49.8%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
	45.5%	(/.f64 (*.f64 #s(approx (sin th) th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	49.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
	38.3%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) #s(approx (sin th) th))
	56.8%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) kx))) (sin.f64 th))
	53.9%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) (sin.f64 th))
	29.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) #s(approx (sin th) th))
	42.7%	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th))
	44.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))))) #s(approx (sin th) th))
✓	91.4%	(*.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))
▶	84.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	85.2%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	47.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	34.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
✓	22.0%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
	22.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) (sin.f64 th))
	17.6%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th))
	31.7%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
▶	20.5%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	53.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
✓	56.7%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	36.0%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
▶	49.5%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	33.4%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	31.2%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 ky))))
▶	34.9%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
	29.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
✓	31.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
✓	15.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))

Compiler

Compiled 1 010 to 730 computations (27.7% saved)

simplify1.1s (7.9%)

Memory

5.3MiB live, 52.0MiB allocated; 3ms collecting garbage

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	513
0	63	509
1	77	509
2	137	509
3	246	509
4	507	509
5	1400	509
6	5000	509
0	8311	509

Stop Event

1×	saturated
1×	node limit
1×	iter limit

Calls

Call 1

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

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

localize849.0ms (6.2%)

Memory

-14.6MiB live, 215.1MiB allocated; 21ms collecting garbage

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.05078125	(hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))
accuracy	0.24609375	(*.f64 (sin.f64 th) (sin.f64 ky))
accuracy	2.9126349285202178	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
accuracy	30.288906365945824	#s(approx (sin ky) ky)
accuracy	0.05078125	(hypot.f64 (sin.f64 kx) (sin.f64 ky))
accuracy	0.21484375	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
accuracy	0.296875	(/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
accuracy	32.2496672933117	#s(approx (sin th) th)
accuracy	0.00390625	(sin.f64 kx)
accuracy	0.21484375	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
accuracy	0.22265625	(/.f64 (sin.f64 th) (sin.f64 kx))
accuracy	43.34313685755039	#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx)))
accuracy	0.19921875	(/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx)))
accuracy	30.288906365945824	#s(approx (sin ky) ky)
accuracy	32.2496672933117	#s(approx (sin th) th)
accuracy	43.489944885919265	#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))
accuracy	0.3170700195368841	(*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))
accuracy	0.455502470470717	(+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))
accuracy	5.131981369608339	(sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))
accuracy	13.77738018369798	(-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx))))

Samples

90.0ms	141×	0	valid
52.0ms	73×	1	valid
42.0ms	42×	2	valid

Compiler

Compiled 485 to 35 computations (92.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-pow2: 29.0ms (22.1% of total)

ival-cos: 23.0ms (17.5% of total)

ival-sin: 22.0ms (16.8% of total)

ival-div: 14.0ms (10.7% of total)

ival-mult: 12.0ms (9.2% of total)

adjust: 11.0ms (8.4% of total)

ival-add: 6.0ms (4.6% of total)

ival-sqrt: 5.0ms (3.8% of total)

ival-hypot: 5.0ms (3.8% of total)

ival-sub: 3.0ms (2.3% of total)

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

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

exact: 0.0ms (0% of total)

series68.0ms (0.5%)

Memory

31.8MiB live, 124.8MiB allocated; 15ms collecting garbage

Counts

23 → 164

Calls

Call 1

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

Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* 1/6 (* (pow kx 2) (sin th)))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (sin th)) (+ (* 1/720 (sin th)) (* 1/6 (+ (* -1/36 (sin th)) (* 1/120 (sin th)))))))) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (sin th)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* 4 (pow kx 2))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* -16/3 (pow kx 2))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 128/45 (pow kx 2)) 16/3))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 128/45 (* -256/315 (pow kx 2)))) 16/3))))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 2))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* -2 (pow kx 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* 2/3 (pow kx 2)) 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 2/3 (* -4/45 (pow kx 2)))) 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 1))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* -4 (pow kx 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 16/3 (pow kx 2)) 4)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 16/3 (* -128/45 (pow kx 2)))) 4)))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (* 2 kx)) 2))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (* 2 kx)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (* 2 kx)) 2)))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (neg (* -2 kx))) 2))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (neg (* -2 kx))))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (neg (* -2 kx))) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* ky (* (sin th) (sqrt 2))) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (* ky (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2))))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2)))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (* (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ 1 (cos (* 2 kx)))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2))))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (sin th))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* (sin ky) (sin th))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ th (sin kx))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* -1/6 (/ (pow th 2) (sin kx))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin kx))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin kx))) (* 1/120 (/ 1 (sin kx))))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (sin ky))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))

Calls

9 calls:

Time	Variable		Point	Expression
12.0ms	kx	@	inf	((* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx 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) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin th) (sin kx)) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
11.0ms	kx	@	-inf	((* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx 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) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin th) (sin kx)) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
9.0ms	ky	@	0	((* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx 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) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin th) (sin kx)) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
6.0ms	th	@	0	((* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx 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) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin th) (sin kx)) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))
6.0ms	ky	@	inf	((* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx 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) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/ (sin th) (sin kx)) (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (sin th) (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (* (sin th) (sin ky)) (sin th) (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx))) (sin kx) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))

simplify966.0ms (7.1%)

Memory

-3.7MiB live, 144.1MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1012	9869
1	2995	9547
0	8350	9485
1	9774	9442
2	12385	9438
3	15236	9438
4	17498	9438
5	18901	9438
6	19777	9438
7	20527	9438
8	21018	9438
9	21329	9438
10	21555	9438
11	21738	9438
12	21865	9438
13	21915	9438
14	21919	9438

Stop Event

1×	saturated
1×	node limit

Counts

164 → 33

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* 1/6 (* (pow kx 2) (sin th)))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (sin th)) (+ (* 1/720 (sin th)) (* 1/6 (+ (* -1/36 (sin th)) (* 1/120 (sin th)))))))) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (sin th)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* 4 (pow kx 2))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* -16/3 (pow kx 2))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 128/45 (pow kx 2)) 16/3))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 128/45 (* -256/315 (pow kx 2)))) 16/3))))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 2))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* -2 (pow kx 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* 2/3 (pow kx 2)) 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 2/3 (* -4/45 (pow kx 2)))) 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 1))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* -4 (pow kx 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 16/3 (pow kx 2)) 4)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 16/3 (* -128/45 (pow kx 2)))) 4)))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (* 2 kx)) 2))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (* 2 kx)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (* 2 kx)) 2)))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (neg (* -2 kx))) 2))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (neg (* -2 kx))))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (neg (* -2 kx))) 2)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* ky (* (sin th) (sqrt 2))) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (* ky (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2))))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2)))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/2 (* (/ (* (pow ky 2) (- 2/45 (* -1/2 (/ (* (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ 1 (cos (* 2 kx)))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2))))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (/ ky (sin kx))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* -1 (* (pow ky 2) (+ (* 1/6 (/ 1 (sin kx))) (* 1/2 (/ 1 (pow (sin kx) 3)))))) (/ 1 (sin kx))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* 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))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow ky 2) (sin th)) (pow (sin kx) 3))) (/ (sin th) (sin kx)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* ky (+ (* (pow ky 2) (+ (* -1/2 (/ (sin th) (pow (sin kx) 3))) (* -1/6 (/ (sin th) (sin kx))))) (/ (sin th) (sin kx))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (sin th))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* -1/6 (* (pow ky 2) (sin th)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* 1/120 (* (pow ky 2) (sin th)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* ky (+ (sin th) (* (pow ky 2) (+ (* -1/6 (sin th)) (* (pow ky 2) (+ (* -1/5040 (* (pow ky 2) (sin th))) (* 1/120 (sin th))))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sin ky) #s(hole binary64 (sin ky)))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* (sin ky) (sin th))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* 1/120 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))) (* (pow th 2) (+ (* -1/6 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* (pow th 2) (+ (* -1/5040 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))) (* 1/120 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ th (sin kx))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* -1/6 (/ (pow th 2) (sin kx))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin kx))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin kx))) (* 1/120 (/ 1 (sin kx))))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (sin ky))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))

Outputs
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) (sin.f64 ky))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (sin 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(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 1))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* -1/2 (/ (pow kx 2) (pow (sin ky) 2))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ (* -1/2 (* (pow kx 2) (* (pow (sin ky) 2) (+ (* -1/2 (/ (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))) (pow (sin ky) 2))) (+ (* 2/45 (/ 1 (pow (sin ky) 4))) (+ (* 2/3 (/ 1 (pow (sin ky) 6))) (/ 1 (pow (sin ky) 8)))))))) (* 1/2 (* (pow (sin ky) 2) (+ (* 1/3 (/ 1 (pow (sin ky) 4))) (* 3/4 (/ 1 (pow (sin ky) 6)))))))) (* 1/2 (/ 1 (pow (sin ky) 2))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (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))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (sin th) (sin ky))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 ky)))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 3))) (/ (sin th) (sin ky)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) kx)))
#s(approx (/ (sin th) (sin kx)) (/.f64 (sin.f64 th) kx))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* 1/6 (* (pow kx 2) (sin th)))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (+ (sin th) (* (pow kx 2) (- (* (pow kx 2) (- (* -1 (* (pow kx 2) (+ (* -1/5040 (sin th)) (+ (* 1/720 (sin th)) (* 1/6 (+ (* -1/36 (sin th)) (* 1/120 (sin th)))))))) (+ (* -1/36 (sin th)) (* 1/120 (sin th))))) (* -1/6 (sin th))))) kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (sin th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (sin th) (* -1/2 (/ (* (pow kx 2) (sin th)) (pow (sin ky) 2))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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)))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (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))))))))))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* 4 (pow kx 2))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* -16/3 (pow kx 2))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* 128/45 (pow kx 2)) 16/3))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (* (pow kx 2) (+ 4 (* (pow kx 2) (- (* (pow kx 2) (+ 128/45 (* -256/315 (pow kx 2)))) 16/3))))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 2))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* -2 (pow kx 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* 2/3 (pow kx 2)) 2)))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 2 (* (pow kx 2) (- (* (pow kx 2) (+ 2/3 (* -4/45 (pow kx 2)))) 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 1))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* -4 (pow kx 2)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* 16/3 (pow kx 2)) 4)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 16/3 (* -128/45 (pow kx 2)))) 4)))))
#s(approx (sin kx) #s(hole binary64 kx))
#s(approx (sin kx) kx)
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* -1/6 (pow kx 2))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* 1/120 (pow kx 2)) 1/6))))))
#s(approx (sin kx) #s(hole binary64 (* kx (+ 1 (* (pow kx 2) (- (* (pow kx 2) (+ 1/120 (* -1/5040 (pow kx 2)))) 1/6))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin ky)))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin ky) (* 1/2 (/ (pow kx 2) (sin ky))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (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))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))) (pow (sin ky) 2)))))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (sin th) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ (sin th) (sin kx))))
#s(approx (/ (sin th) (sin kx)) (/.f64 (sin.f64 th) (sin.f64 kx)))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (* 2 kx)) 2))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (*.f64 (sin.f64 (+.f64 kx kx)) (sin.f64 (+.f64 kx kx))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (* 2 kx)))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (* 2 kx)) 2)))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx))))
#s(approx (sin kx) #s(hole binary64 (sin kx)))
#s(approx (sin kx) (sin.f64 kx))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))))
#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* (sin ky) (sin th)) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (sin ky) (sqrt (/ 1 (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (sqrt (+ (* 1/2 (/ (- 1 (pow (cos (neg (* -2 kx))) 2)) (+ 1 (cos (neg (* -2 kx)))))) (pow (sin ky) 2)))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) #s(hole binary64 (- 1 (pow (cos (neg (* -2 kx))) 2))))
#s(approx (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (*.f64 (sin.f64 (+.f64 kx kx)) (sin.f64 (+.f64 kx kx))))
#s(approx (+ (cos (- kx kx)) (cos (+ kx kx))) #s(hole binary64 (+ 1 (cos (neg (* -2 kx))))))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) #s(hole binary64 (pow (cos (neg (* -2 kx))) 2)))
#s(approx (* (cos (+ kx kx)) (cos (+ kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* (* ky (* (sin th) (sqrt 2))) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (* (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) (sin th)) #s(hole binary64 (* ky (+ (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (sin th) (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ (sin th) (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (* (sin th) (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (* (sin th) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* (* ky (sqrt 2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))))))))))))
#s(approx (/ (sin ky) (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2)))) #s(hole binary64 (* ky (+ (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2))))) (* (pow ky 2) (+ (* -2 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/6 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* 1/120 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (+ (* 1/3 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (* (pow ky 2) (+ (* -1/2 (* (/ (+ (* -2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))))) (- 1 (pow (cos (* 2 kx)) 2)))) (+ (* 8/45 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (+ (* 2 (/ (* (+ 1 (cos (* 2 kx))) (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))))) (* (pow (sqrt 2) 2) (- 1 (pow (cos (* 2 kx)) 2))))) (* 8/3 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))) (+ (* -1/60 (* (/ 1 (sqrt 2)) (sqrt (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))))) (+ (* -1/5040 (* (sqrt 2) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/12 (* (/ (+ (* -8 (/ (pow (+ 1 (cos (* 2 kx))) 3) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3))) (+ (* -4/3 (/ (pow (+ 1 (cos (* 2 kx))) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 2))) (* 4 (/ (pow (+ 1 (cos (* 2 kx))) 3) (* (pow (sqrt 2) 2) (pow (- 1 (pow (cos (* 2 kx)) 2)) 3)))))) (sqrt 2)) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))))))))))))))))
#s(approx (sin ky) #s(hole binary64 ky))
#s(approx (sin ky) ky)
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* -1/6 (pow ky 2))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* 1/120 (pow ky 2)) 1/6))))))
#s(approx (sin ky) #s(hole binary64 (* ky (+ 1 (* (pow ky 2) (- (* (pow ky 2) (+ 1/120 (* -1/5040 (pow ky 2)))) 1/6))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* 1/2 (* (/ (pow ky 2) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))))))
#s(approx (sqrt (+ (/ (/ (- (* (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (+ (cos (- kx kx)) (cos (+ kx kx)))) 2) (pow (sin ky) 2))) #s(hole binary64 (+ (* (sqrt 1/2) (sqrt (/ (- 1 (pow (cos (* 2 kx)) 2)) (+ 1 (cos (* 2 kx)))))) (* (pow ky 2) (+ (* -1/2 (* (/ (* (pow ky 2) (+ 1/3 (* 1/4 (/ (+ 1 (cos (* 2 kx))) (* (pow (sqrt 1/2) 2) (- 1 (pow (cos (* 2 kx)) 2))))))) (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))) (* 1/2 (* (/ 1 (sqrt 1/2)) (sqrt (/ (+ 1 (cos (* 2 kx))) (- 1 (pow (cos (* 2 kx)) 2)))))))))))
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#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (+ (* (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)))))
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#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (/ (* ky (sin th)) (sin kx))))
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#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (sin kx)))
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#s(approx (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))) #s(hole binary64 (+ (sin kx) (* 1/2 (/ (pow ky 2) (sin kx))))))
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#s(approx (sin ky) #s(hole binary64 (sin ky)))
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#s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) (sin.f64 th)))
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#s(approx (* (sin ky) (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky)))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
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#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
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#s(approx (/ (sin th) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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)))))))))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (/ th (sin kx))))
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#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* -1/6 (/ (pow th 2) (sin kx))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* 1/120 (/ (pow th 2) (sin kx))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (/ (sin th) (sin kx)) #s(hole binary64 (* th (+ (* (pow th 2) (- (* (pow th 2) (+ (* -1/5040 (/ (pow th 2) (sin kx))) (* 1/120 (/ 1 (sin kx))))) (* 1/6 (/ 1 (sin kx))))) (/ 1 (sin kx))))))
#s(approx (sin th) #s(hole binary64 th))
#s(approx (sin th) th)
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* -1/6 (pow th 2))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* 1/120 (pow th 2)) 1/6))))))
#s(approx (sin th) #s(hole binary64 (* th (+ 1 (* (pow th 2) (- (* (pow th 2) (+ 1/120 (* -1/5040 (pow th 2)))) 1/6))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* (* th (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* th (+ (* -1/6 (* (* (pow th 2) (sin ky)) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))) (* (sin ky) (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))
#s(approx (/ (* (sin th) (sin ky)) (sqrt (+ (* (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(hole binary64 (* 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))))))))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (sin ky))))
#s(approx (* (sin th) (sin ky)) (*.f64 (sin.f64 ky) th))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* -1/6 (* (pow th 2) (sin ky)))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* 1/120 (* (pow th 2) (sin ky)))))))))
#s(approx (* (sin th) (sin ky)) #s(hole binary64 (* th (+ (sin ky) (* (pow th 2) (+ (* -1/6 (sin ky)) (* (pow th 2) (+ (* -1/5040 (* (pow th 2) (sin ky))) (* 1/120 (sin ky))))))))))
#s(approx (sin th) #s(hole binary64 (sin th)))
#s(approx (sin th) (sin.f64 th))

rewrite70.0ms (0.5%)

Memory

3.5MiB live, 49.6MiB allocated; 2ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	340
1	63	340
2	70	340
3	80	340
4	86	340
5	88	340
6	90	340
7	92	334
8	94	334
9	96	334
10	98	334
11	100	334
0	100	293
0	297	293
1	441	293
2	557	293
3	614	293
4	636	293
5	639	293

Stop Event

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

Counts

23 → 60

Calls

Call 1

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

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

eval15.0ms (0.1%)

Memory: -24.3MiB live, 21.5MiB allocated; 4ms collecting garbage
Compiler: Compiled 2 887 to 389 computations (86.5% saved)

prune27.0ms (0.2%)

Memory

-3.5MiB live, 43.0MiB allocated; 2ms collecting garbage

Pruning

40 alts after pruning (28 fresh and 12 done)

	Pruned	Kept	Total
New	97	12	109
Fresh	0	16	16
Picked	2	3	5
Done	2	9	11
Total	101	40	141

Accuracy

99.9%

Counts

141 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	95.5%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
	32.0%	(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky)))
	62.1%	(/.f64 (*.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
	45.5%	(/.f64 (*.f64 #s(approx (sin th) th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	99.6%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	49.5%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
	38.3%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) #s(approx (sin th) th))
	56.8%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) kx))) (sin.f64 th))
	53.9%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) (sin.f64 th))
	29.7%	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) #s(approx (sin th) th))
	42.7%	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th))
	44.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))))) #s(approx (sin th) th))
✓	91.4%	(*.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))
	39.2%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64))))) (sin.f64 th))
	84.9%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (-.f64 kx kx) (+.f64 kx kx)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (-.f64 kx kx) (+.f64 kx kx)) #s(literal 2 binary64)))))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	91.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 #s(approx (- ( (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (*.f64 (sin.f64 (+.f64 kx kx)) (sin.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	85.2%	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
	47.1%	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
✓	34.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
	22.9%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) (sin.f64 th))
	17.6%	(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th))
	31.7%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
✓	20.5%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
	17.1%	(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th))
	9.8%	(.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) #s(approx (sin th) th))
✓	99.6%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	53.9%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	36.0%	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
✓	49.5%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	29.7%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
	33.4%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
	44.9%	(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
	31.2%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 ky))))
✓	34.9%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
	22.9%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) #s(approx (sin kx) kx))))
	21.9%	(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (/ (sin th) (sin kx)) (/.f64 th (sin.f64 kx)))))
	31.7%	(.f64 #s(approx (sin ky) ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
	29.7%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
✓	31.2%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
✓	15.8%	#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))

Compiler

Compiled 1 962 to 805 computations (59% saved)

regimes122.0ms (0.9%)

Memory

25.5MiB live, 168.3MiB allocated; 12ms collecting garbage

Counts

51 → 1

Calls

Call 1

Inputs
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))
(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))
(.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky)))) (sin.f64 ky))) #s(approx (sin th) th))
(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (*.f64 (sin.f64 th) ky) (sin.f64 kx)))
(.f64 #s(approx (sin ky) ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(*.f64 #s(approx (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (/.f64 ky (sin.f64 kx))) (sin.f64 th))
(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) #s(approx (/ (sin th) (sin kx)) (/.f64 th (sin.f64 kx)))))
(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) #s(approx (sin kx) kx))))
(*.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th))
(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx))))
(.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) #s(approx (sin th) th))
(/.f64 (*.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky))))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 #s(approx (sin ky) ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) #s(approx (sin kx) kx))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) #s(approx (sin th) th))
(/.f64 (*.f64 #s(approx (sin th) th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky)))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 #s(approx (pow (sin kx) 2) (.f64 kx kx)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 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) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(/.f64 (*.f64 (sin.f64 th) (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
(*.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (.f64 (sin.f64 ky) (sin.f64 ky))))) #s(approx (sin th) th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(approx (sin th) th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) #s(approx (sin th) th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (fma.f64 (sin.f64 kx) (sin.f64 kx) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (-.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (exp.f64 (log.f64 (sin.f64 kx))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 #s(approx (- ( (cos (- kx kx)) (cos (- kx kx))) (* (cos (+ kx kx)) (cos (+ kx kx)))) (*.f64 (sin.f64 (+.f64 kx kx)) (sin.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 #s(approx (sin ky) ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (cosh.f64 (.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 (sin.f64 kx)) #s(literal 2 binary64)))) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (*.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (+.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (/.f64 (/.f64 (-.f64 (.f64 (cos.f64 (-.f64 kx kx)) (cos.f64 (-.f64 kx kx))) (.f64 (cos.f64 (+.f64 kx kx)) (cos.f64 (+.f64 kx kx)))) (.f64 #s(literal 2 binary64) (*.f64 (cos.f64 (/.f64 (+.f64 (-.f64 kx kx) (+.f64 kx kx)) #s(literal 2 binary64))) (cos.f64 (/.f64 (-.f64 (-.f64 kx kx) (+.f64 kx kx)) #s(literal 2 binary64)))))) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
(*.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))) (sin.f64 th))
(.f64 (/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (fma.f64 (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (.f64 (pow.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (-.f64 (pow.f64 (sin.f64 ky) #s(literal 2 binary64)) (pow.f64 (sin.f64 kx) #s(literal 2 binary64))) (pow.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) #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:

17.0ms	kx
14.0ms	(sin.f64 ky)
14.0ms	(sin.f64 th)
13.0ms	(*.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))
13.0ms	th

Results

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

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes89.0ms (0.7%)

Memory

-19.7MiB live, 123.0MiB allocated; 13ms collecting garbage

Counts

34 → 1

Calls

Call 1

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

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

Calls

9 calls:

12.0ms	(sin.f64 th)
12.0ms	ky
12.0ms	(sin.f64 ky)
9.0ms	kx
9.0ms	th

Results

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

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes85.0ms (0.6%)

Memory

28.1MiB live, 118.4MiB allocated; 8ms collecting garbage

Counts

33 → 2

Calls

Call 1

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

Calls

9 calls:

11.0ms	kx
10.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
9.0ms	(sin.f64 ky)
9.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
9.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
80.8%	3	`(sin.f64 th)`
78.9%	4	`(sin.f64 kx)`
75.3%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
79.1%	4	`(sin.f64 ky)`
83.3%	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)))))`
74.3%	4	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
75.3%	2	`kx`
76.9%	3	`ky`
80.8%	2	`th`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes76.0ms (0.6%)

Memory

2.0MiB live, 51.7MiB allocated; 10ms collecting garbage

Counts

23 → 2

Calls

Call 1

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

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

Calls

9 calls:

24.0ms	(sin.f64 ky)
7.0ms	(sin.f64 th)
6.0ms	th
6.0ms	kx
6.0ms	(*.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
64.7%	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))`
62.1%	1	`ky`
63.8%	2	`kx`
62.1%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
63.9%	2	`(sin.f64 kx)`
67.8%	2	`(sin.f64 ky)`
70.0%	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)))))`
69.2%	3	`(sin.f64 th)`
69.1%	2	`th`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes763.0ms (5.6%)

Memory

-11.9MiB live, 79.2MiB allocated; 5ms collecting garbage

Counts

21 → 4

Calls

Call 1

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

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

Calls

9 calls:

713.0ms	(sin.f64 ky)
7.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))
6.0ms	kx
6.0ms	(sin.f64 th)
6.0ms	(sin.f64 kx)

Results

Accuracy	Segments	Branch
48.8%	2	`ky`
50.9%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
50.9%	2	`kx`
53.7%	3	`(sin.f64 kx)`
53.8%	4	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
51.9%	4	`(sin.f64 th)`
54.1%	3	`(sin.f64 ky)`
65.4%	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)))))`
52.6%	3	`th`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes6.0ms (0%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

19 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
62.8%	3	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes6.0ms (0%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Counts

17 → 2

Calls

Call 1

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

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:

5.0ms

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

Results

Accuracy	Segments	Branch
58.0%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes6.0ms (0%)

Memory

7.4MiB live, 7.4MiB allocated; 0ms collecting garbage

Counts

16 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
58.0%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes37.0ms (0.3%)

Memory

-32.9MiB live, 12.2MiB allocated; 5ms collecting garbage

Counts

14 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

36.0ms

(/.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
55.9%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes3.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Counts

7 → 2

Calls

Call 1

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

Outputs

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

3.0ms

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

Results

Accuracy	Segments	Branch
54.7%	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)

regimes342.0ms (2.5%)

Memory

-14.6MiB live, 39.5MiB allocated; 25ms collecting garbage

Counts

6 → 2

Calls

Call 1

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

Outputs

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

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

Calls

9 calls:

322.0ms	(sin.f64 th)
3.0ms	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	(sin.f64 kx)
2.0ms	(sin.f64 ky)

Results

Accuracy	Segments	Branch
40.0%	2	`ky`
37.2%	3	`(sin.f64 th)`
43.1%	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))`
41.4%	2	`kx`
41.4%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
37.2%	2	`th`
42.1%	3	`(sin.f64 kx)`
39.9%	2	`(sin.f64 ky)`
46.9%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes2.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated; 0ms collecting garbage

Counts

4 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

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
43.2%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 13 to 11 computations (15.4% saved)

regimes13.0ms (0.1%)

Memory

29.6MiB live, 29.6MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs

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

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

Outputs

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

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

Calls

9 calls:

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

Results

Accuracy	Segments	Branch
20.8%	2	`(sin.f64 th)`
20.8%	2	`th`
24.2%	2	`(sin.f64 ky)`
24.5%	2	`ky`
23.7%	3	`(sin.f64 kx)`
23.6%	2	`kx`
23.6%	2	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
26.1%	2	`(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))`
27.8%	2	`(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))`

Compiler

Compiled 42 to 51 computations (-21.4% saved)

regimes13.0ms (0.1%)

Memory

-20.7MiB live, 24.3MiB allocated; 4ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

9 calls:

4.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) (sin.f64 th))
1.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64)))))
1.0ms	ky
1.0ms	(sin.f64 ky)
1.0ms	(pow.f64 (sin.f64 kx) #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
15.8%	1	`th`
15.8%	1	`(sin.f64 th)`
15.8%	1	`(sin.f64 kx)`
15.8%	1	`kx`
15.8%	1	`(pow.f64 (sin.f64 kx) #s(literal 2 binary64))`
15.8%	1	`(sin.f64 ky)`
15.8%	1	`ky`
15.8%	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))`
15.8%	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)

bsearch22.0ms (0.2%)

Memory

24.2MiB live, 24.2MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	8.704363636804978e-6	0.006740972125707429

Samples

15.0ms

128×

valid

Compiler

Compiled 243 to 194 computations (20.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sin: 7.0ms (60.3% of total)

ival-pow2: 2.0ms (17.2% of total)

ival-div: 1.0ms (8.6% of total)

ival-add: 1.0ms (8.6% of total)

ival-mult: 1.0ms (8.6% of total)

ival-sqrt: 1.0ms (8.6% of total)

adjust: 0.0ms (0% of total)

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

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

bsearch38.0ms (0.3%)

Memory

-36.2MiB live, 10.2MiB allocated; 2ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
36.0ms	7.131540827154818e-93	3.8671709757610396e-92

Samples

33.0ms

96×

valid

Compiler

Compiled 199 to 156 computations (21.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sin: 26.0ms (86.5% of total)

ival-pow2: 2.0ms (6.7% of total)

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

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

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

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

adjust: 0.0ms (0% of total)

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

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

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	1.0022104839143322	+inf
0.0ms	1.9892470438882938e-12	8.168693266844843e-6
0.0ms	-0.9999999999999999	-0.999791706548765

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6
0.0ms	-0.9999999999999999	-0.999791706548765

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.9892470438882938e-12	8.168693266844843e-6

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.1328583376836177e-25	2.529282656267466e-24

Compiler

Compiled 19 to 19 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.1328583376836177e-25	2.529282656267466e-24

Compiler

Compiled 19 to 19 computations (0% saved)

simplify62.0ms (0.5%)

Memory

17.7MiB live, 64.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	795
1	129	795
2	192	795
3	303	795
4	580	795
5	1752	795
6	7872	795

Stop Event

1×	node 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) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(if (<=.f64 th #s(literal 112986307451471/2305843009213693952 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(if (<=.f64 th #s(literal 8807034685401875/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -2251349453722511/2251799813685248 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky)))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -2251349453722511/2251799813685248 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 #s(approx (sin ky) ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))

Outputs
(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
(if (<=.f64 th #s(literal 112986307451471/2305843009213693952 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(if (<=.f64 th #s(literal 8807034685401875/1174271291386916613944740298394668513687841274454159935353645485766104512557304221731849499192384351515967488 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (/.f64 (.f64 (sin.f64 th) #s(approx (sin ky) ky)) (hypot.f64 (sin.f64 kx) #s(approx (sin ky) ky))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -2251349453722511/2251799813685248 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 2 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)) (*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 #s(approx (sin kx) kx) #s(approx (sin ky) ky)))))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal -2251349453722511/2251799813685248 binary64)) (.f64 (sin.f64 ky) (/.f64 #s(approx (sin th) th) (hypot.f64 #s(approx (sin kx) kx) (sin.f64 ky)))) (if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th))))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 (sin.f64 ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) (sin.f64 th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (sin.f64 ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 #s(approx (sin ky) ky) #s(approx (/ (sin th) (sqrt (+ ( (sin kx) (sin kx)) (* (sin ky) (sin ky))))) (/.f64 (sin.f64 th) (sin.f64 kx)))) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) #s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (/.f64 (.f64 (sin.f64 th) ky) (sin.f64 kx))) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 4951760157141521/2475880078570760549798248448 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) (sin.f64 kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) (sin.f64 th)))
(if (<=.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) #s(literal 2 binary64)) (pow.f64 (sin.f64 ky) #s(literal 2 binary64))))) #s(literal 5444517870735015/10889035741470030830827987437816582766592 binary64)) (.f64 (/.f64 #s(approx (sin ky) ky) #s(approx (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2))) #s(approx (sin kx) kx))) #s(approx (sin th) th)) #s(approx ( (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th)))
#s(approx (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)) #s(approx (sin th) th))

derivations528.0ms (3.9%)

Memory

-6.2MiB live, 364.8MiB allocated; 62ms collecting garbage

Stop Event

1×

fuel

Compiler

Compiled 723 to 88 computations (87.8% saved)

preprocess80.0ms (0.6%)

Memory

24.7MiB live, 125.4MiB allocated; 11ms collecting garbage

Remove

(negabs ky)

(negabs th)

(abs kx)

Compiler

Compiled 1 544 to 256 computations (83.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Iter	Nodes	Cost
0	18	65
1	25	65
2	31	65
3	35	59
4	37	59
5	39	59
6	41	59
7	43	59
0	43	59
1	80	59
0	362	36
1	509	36
2	680	36
3	833	36
4	896	36
5	908	36
6	909	36

Iter	Nodes	Cost
0	42	208
1	52	208
2	59	208
3	72	208
4	78	208
5	84	202
6	86	202
7	88	202
8	90	202
9	92	202
0	92	160
0	236	159
1	357	159
2	424	159
3	456	159
4	467	159
5	469	159

Iter	Nodes	Cost
0	53	340
1	63	340
2	70	340
3	80	340
4	86	340
5	88	340
6	90	340
7	92	334
8	94	334
9	96	334
10	98	334
11	100	334
0	100	293
0	297	293
1	441	293
2	557	293
3	614	293
4	636	293
5	639	293

Iter	Nodes	Cost
0	18	65
1	25	65
2	31	65
3	35	59
4	37	59
5	39	59
6	41	59
7	43	59
0	43	59
1	80	59
0	362	36
1	509	36
2	680	36
3	833	36
4	896	36
5	908	36
6	909	36

Iter	Nodes	Cost
0	42	208
1	52	208
2	59	208
3	72	208
4	78	208
5	84	202
6	86	202
7	88	202
8	90	202
9	92	202
0	92	160
0	236	159
1	357	159
2	424	159
3	456	159
4	467	159
5	469	159

Iter	Nodes	Cost
0	53	340
1	63	340
2	70	340
3	80	340
4	86	340
5	88	340
6	90	340
7	92	334
8	94	334
9	96	334
10	98	334
11	100	334
0	100	293
0	297	293
1	441	293
2	557	293
3	614	293
4	636	293
5	639	293

start0.0ms (0%)

analyze194.0ms (1.4%)

sample4.0s (29.8%)

explain207.0ms (1.5%)

preprocess375.0ms (2.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify125.0ms (0.9%)

localize391.0ms (2.9%)

series34.0ms (0.2%)

simplify520.0ms (3.8%)

rewrite70.0ms (0.5%)

eval9.0ms (0.1%)

prune48.0ms (0.4%)

simplify96.0ms (0.7%)

localize182.0ms (1.3%)

series90.0ms (0.7%)

simplify834.0ms (6.1%)

rewrite41.0ms (0.3%)

eval21.0ms (0.2%)

prune20.0ms (0.2%)

simplify102.0ms (0.8%)

localize97.0ms (0.7%)

series26.0ms (0.2%)

simplify468.0ms (3.4%)

rewrite87.0ms (0.6%)

eval51.0ms (0.4%)

prune78.0ms (0.6%)

simplify1.1s (7.9%)

localize849.0ms (6.2%)

series68.0ms (0.5%)

simplify966.0ms (7.1%)

rewrite70.0ms (0.5%)

eval15.0ms (0.1%)

prune27.0ms (0.2%)

regimes122.0ms (0.9%)

regimes89.0ms (0.7%)

regimes85.0ms (0.6%)

regimes76.0ms (0.6%)

regimes763.0ms (5.6%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes6.0ms (0%)

regimes37.0ms (0.3%)

regimes3.0ms (0%)

regimes342.0ms (2.5%)

regimes2.0ms (0%)

regimes13.0ms (0.1%)

regimes13.0ms (0.1%)

bsearch22.0ms (0.2%)

bsearch38.0ms (0.3%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify62.0ms (0.5%)

derivations528.0ms (3.9%)

preprocess80.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	65
1	25	65
2	31	65
3	35	59
4	37	59
5	39	59
6	41	59
7	43	59
0	43	59
1	80	59
0	362	36
1	509	36
2	680	36
3	833	36
4	896	36
5	908	36
6	909	36

Iter	Nodes	Cost
0	42	208
1	52	208
2	59	208
3	72	208
4	78	208
5	84	202
6	86	202
7	88	202
8	90	202
9	92	202
0	92	160
0	236	159
1	357	159
2	424	159
3	456	159
4	467	159
5	469	159

Iter	Nodes	Cost
0	53	340
1	63	340
2	70	340
3	80	340
4	86	340
5	88	340
6	90	340
7	92	334
8	94	334
9	96	334
10	98	334
11	100	334
0	100	293
0	297	293
1	441	293
2	557	293
3	614	293
4	636	293
5	639	293